 7.1: use a reciprocal identity to nd the function value indicated. Ratio...
 7.2: use a reciprocal identity to nd the function value indicated. Ratio...
 7.3: use a reciprocal identity to nd the function value indicated. Ratio...
 7.4: use a reciprocal identity to nd the function value indicated. Ratio...
 7.5: use a reciprocal identity to nd the function value indicated. Ratio...
 7.6: use a reciprocal identity to nd the function value indicated. Ratio...
 7.7: use a reciprocal identity to nd the function value indicated. Ratio...
 7.8: use a reciprocal identity to nd the function value indicated. Ratio...
 7.9: use a reciprocal identity to nd the function value indicated. Ratio...
 7.10: use a reciprocal identity to nd the function value indicated. Ratio...
 7.11: use a reciprocal identity to nd the function value indicated. Ratio...
 7.12: use a reciprocal identity to nd the function value indicated. Ratio...
 7.13: use a quotient identity to nd the function value indicated. Rationa...
 7.14: use a quotient identity to nd the function value indicated. Rationa...
 7.15: use a quotient identity to nd the function value indicated. Rationa...
 7.16: use a quotient identity to nd the function value indicated. Rationa...
 7.17: use a quotient identity to nd the function value indicated. Rationa...
 7.18: use a quotient identity to nd the function value indicated. Rationa...
 7.19: use a quotient identity to nd the function value indicated. Rationa...
 7.20: use a quotient identity to nd the function value indicated. Rationa...
 7.21: nd the indicated expression. If nd
 7.22: nd the indicated expression. If nd
 7.23: nd the indicated expression. If nd
 7.24: nd the indicated expression.
 7.25: nd the indicated expression.
 7.26: nd the indicated expression.
 7.27: use a Pythagorean identity to nd the function value indicated. Rati...
 7.28: use a Pythagorean identity to nd the function value indicated. Rati...
 7.29: use a Pythagorean identity to nd the function value indicated. Rati...
 7.30: use a Pythagorean identity to nd the function value indicated. Rati...
 7.31: use a Pythagorean identity to nd the function value indicated. Rati...
 7.32: use a Pythagorean identity to nd the function value indicated. Rati...
 7.33: use a Pythagorean identity to nd the function value indicated. Rati...
 7.34: use a Pythagorean identity to nd the function value indicated. Rati...
 7.35: use a Pythagorean identity to nd the function value indicated. Rati...
 7.36: use a Pythagorean identity to nd the function value indicated. Rati...
 7.37: use a Pythagorean identity to nd the function value indicated. Rati...
 7.38: use a Pythagorean identity to nd the function value indicated. Rati...
 7.39: use a Pythagorean identity to nd the function value indicated. Rati...
 7.40: use a Pythagorean identity to nd the function value indicated. Rati...
 7.41: use a Pythagorean identity to nd the function value indicated. Rati...
 7.42: use a Pythagorean identity to nd the function value indicated. Rati...
 7.43: use a Pythagorean identity to nd the function value indicated. Rati...
 7.44: use a Pythagorean identity to nd the function value indicated. Rati...
 7.45: use a Pythagorean identity to nd the function value indicated. Rati...
 7.46: use a Pythagorean identity to nd the function value indicated. Rati...
 7.47: use identities to nd the function values indicated. Rationalize the...
 7.48: use identities to nd the function values indicated. Rationalize the...
 7.49: use identities to nd the function values indicated. Rationalize the...
 7.50: use identities to nd the function values indicated. Rationalize the...
 7.51: use identities to nd the function values indicated. Rationalize the...
 7.52: use identities to nd the function values indicated. Rationalize the...
 7.53: use identities to nd the function values indicated. Rationalize the...
 7.54: use identities to nd the function values indicated. Rationalize the...
 7.55: use identities to nd the function values indicated. Rationalize the...
 7.56: use identities to nd the function values indicated. Rationalize the...
 7.57: perform the indicated operations and simplify your answers, if poss...
 7.58: perform the indicated operations and simplify your answers, if poss...
 7.59: perform the indicated operations and simplify your answers, if poss...
 7.60: perform the indicated operations and simplify your answers, if poss...
 7.61: perform the indicated operations and simplify your answers, if poss...
 7.62: perform the indicated operations and simplify your answers, if poss...
 7.63: perform the indicated operations and simplify your answers, if poss...
 7.64: perform the indicated operations and simplify your answers, if poss...
 7.65: perform the indicated operations and simplify your answers, if poss...
 7.66: perform the indicated operations and simplify your answers, if poss...
 7.67: perform the indicated operations and simplify your answers, if poss...
 7.68: perform the indicated operations and simplify your answers, if poss...
 7.69: perform the indicated operations and simplify your answers, if poss...
 7.70: perform the indicated operations and simplify your answers, if poss...
 7.71: refer to the following: The bifolium is a curve that can be drawn u...
 7.72: refer to the following: The bifolium is a curve that can be drawn u...
 7.73: refer to the following: The monthly revenues (measured in thousands...
 7.74: refer to the following: The monthly revenues (measured in thousands...
 7.75: explain the mistake that is made. If and the terminal side of lies ...
 7.76: explain the mistake that is made. Find and if and the terminal side...
 7.77: determine whether each statement is true or false. It is possible f...
 7.78: determine whether each statement is true or false. It is possible f...
 7.79: Find the measure of an angle , , which satises the equation sinu = ...
 7.80: Find the measure of an angle , , which satises the equation .
 7.81: Write only in terms of .
 7.82: Write only in terms of .
 7.83: Let in the expression and simplify.
 7.84: Let in the expression and simplify
 7.85: Let in the expression and simplify
 7.86: Simplify cos2 u cos2 u 1# 1  csc2 u tan2 u  sec2 u.
 7.87: determine whether each statement is true or false. sec2 u 1, for al...
 7.88: determine whether each statement is true or false. 1  csc2u 7 0, f...
 7.89: Verify the quotient numerically for Use a calculator to nda. b. c. ...
 7.90: Is ? Use a calculator to nda. b. c. d.Are the results in (c) and (d...
 7.91: Does ? Use a calculator to nd: a. b. c. Which results are the same?
 7.92: Does ? Use a calculator to nd: a. b. c.Which results are the same?
 7.1: simplify each of the trigonometric expressions.
 7.2: simplify each of the trigonometric expressions.
 7.3: simplify each of the trigonometric expressions.
 7.4: simplify each of the trigonometric expressions.
 7.5: simplify each of the trigonometric expressions.
 7.6: simplify each of the trigonometric expressions.
 7.7: simplify each of the trigonometric expressions.
 7.8: simplify each of the trigonometric expressions.
 7.9: simplify each of the trigonometric expressions.
 7.10: simplify each of the trigonometric expressions.
 7.11: simplify each of the trigonometric expressions.
 7.12: simplify each of the trigonometric expressions.
 7.13: simplify each of the trigonometric expressions.
 7.14: simplify each of the trigonometric expressions.
 7.15: simplify each of the trigonometric expressions.
 7.16: simplify each of the trigonometric expressions.
 7.17: simplify each of the trigonometric expressions.
 7.18: simplify each of the trigonometric expressions.
 7.19: simplify each of the trigonometric expressions.
 7.20: simplify each of the trigonometric expressions.
 7.21: simplify each of the trigonometric expressions.
 7.22: simplify each of the trigonometric expressions.
 7.23: simplify each of the trigonometric expressions.
 7.24: simplify each of the trigonometric expressions.
 7.25: verify each of the trigonometric identities.
 7.26: verify each of the trigonometric identities.(1  sinx)(1 + sinx) = ...
 7.27: verify each of the trigonometric identities.
 7.28: verify each of the trigonometric identities.(sec x + 1)(sec x  1) ...
 7.29: verify each of the trigonometric identities.
 7.30: verify each of the trigonometric identities.cscx  sinx = cotx cos
 7.31: verify each of the trigonometric identities.
 7.32: verify each of the trigonometric identities.2  cos2 x sin x = csc ...
 7.33: verify each of the trigonometric identities.
 7.34: verify each of the trigonometric identities.tan(x) cot(x) =1
 7.35: verify each of the trigonometric identities.
 7.36: verify each of the trigonometric identities.csc(x)  1 =cot2 x csc...
 7.37: verify each of the trigonometric identities.
 7.38: verify each of the trigonometric identities.ot2 x 1 tan2 x = sec2 x...
 7.39: verify each of the trigonometric identities.
 7.40: verify each of the trigonometric identities.1 1cosx+1 1 +cosx= 2 c...
 7.41: verify each of the trigonometric identities.
 7.42: verify each of the trigonometric identities.cos2 x 1  sinx= 1 + sinx
 7.43: verify each of the trigonometric identities.
 7.44: verify each of the trigonometric identities.cscx + cotx =1 cscx  cotx
 7.45: verify each of the trigonometric identities.
 7.46: verify each of the trigonometric identities.secx + tanx cscx + 1= tanx
 7.47: verify each of the trigonometric identities.
 7.48: verify each of the trigonometric identities.sin x + 1  cos2 x cos2...
 7.49: verify each of the trigonometric identities.
 7.50: verify each of the trigonometric identities.tanx(cscx  sinx) = cosx
 7.51: determine whether each equation is an identity, a conditional equat...
 7.52: determine whether each equation is an identity, a conditional equat...
 7.53: determine whether each equation is an identity, a conditional equat...
 7.54: determine whether each equation is an identity, a conditional equat...
 7.55: determine whether each equation is an identity, a conditional equat...
 7.56: determine whether each equation is an identity, a conditional equat...
 7.57: determine whether each equation is an identity, a conditional equat...
 7.58: determine whether each equation is an identity, a conditional equat...
 7.59: determine whether each equation is an identity, a conditional equat...
 7.60: determine whether each equation is an identity, a conditional equat...
 7.61: determine whether each equation is an identity, a conditional equat...
 7.62: determine whether each equation is an identity, a conditional equat...
 7.63: determine whether each equation is an identity, a conditional equat...
 7.64: determine whether each equation is an identity, a conditional equat...
 7.65: refer to the following: In calculus, when integrating expressions s...
 7.66: refer to the following: In calculus, when integrating expressions s...
 7.67: explain the mistake that is made.erify the identity Solution: Start...
 7.68: explain the mistake that is made.Verify the identity Solution: Star...
 7.69: explain the mistake that is made.Determine whether the equation is ...
 7.70: explain the mistake that is made. Determine whether the equation is...
 7.71: determine whether each statement is true or false. If an equation i...
 7.72: determine whether each statement is true or false. If an equation h...
 7.73: In which quadrants is the equation true?
 7.74: In which quadrants is the equation true?
 7.75: In which quadrants is the equation true?
 7.76: In which quadrants is the equation true?
 7.77: Simplify .
 7.78: Simplify
 7.79: Do you think that Why?
 7.80: Do you think that Why?
 7.81: Do you think
 7.82: Do you think cot(A2) = (cot A)2? Why?
 7.83: In the next section you will learn the sum and difference identitie...
 7.84: In the next section you will learn the sum and difference identitie...
 7.85: In the next section you will learn the sum and difference identitie...
 7.86: In the next section you will learn the sum and difference identitie...
 7.87: In the next section you will learn the sum and difference identitie...
 7.88: In the next section you will learn the sum and difference identitie...
 7.89: In the next section you will learn the sum and difference identitie...
 7.90: In the next section you will learn the sum and difference identitie...
 7.1: nd the exact value for each trigonometric expression.sin ap 12b
 7.2: nd the exact value for each trigonometric expression.cos ap 12b
 7.3: nd the exact value for each trigonometric expression.cos a5p 12b
 7.4: nd the exact value for each trigonometric expression.
 7.5: nd the exact value for each trigonometric expression.
 7.6: nd the exact value for each trigonometric expression.
 7.7: nd the exact value for each trigonometric expression.
 7.8: nd the exact value for each trigonometric expression.
 7.9: nd the exact value for each trigonometric expression.
 7.10: nd the exact value for each trigonometric expression.
 7.11: nd the exact value for each trigonometric expression.
 7.12: nd the exact value for each trigonometric expression.
 7.13: nd the exact value for each trigonometric expression.
 7.14: nd the exact value for each trigonometric expression.
 7.15: nd the exact value for each trigonometric expression.csc(255)
 7.16: nd the exact value for each trigonometric expression.csc(15)
 7.17: write each expression as a single trigonometric function.
 7.18: write each expression as a single trigonometric function.
 7.19: write each expression as a single trigonometric function.
 7.20: write each expression as a single trigonometric function.
 7.21: write each expression as a single trigonometric function.
 7.22: write each expression as a single trigonometric function.
 7.23: write each expression as a single trigonometric function.
 7.24: write each expression as a single trigonometric function.
 7.25: write each expression as a single trigonometric function.
 7.26: write each expression as a single trigonometric function.
 7.27: write each expression as a single trigonometric function.
 7.28: write each expression as a single trigonometric function.
 7.29: nd the exact value of the indicated expression using the given info...
 7.30: nd the exact value of the indicated expression using the given info...
 7.31: nd the exact value of the indicated expression using the given info...
 7.32: nd the exact value of the indicated expression using the given info...
 7.33: nd the exact value of the indicated expression using the given info...
 7.34: nd the exact value of the indicated expression using the given info...
 7.35: determine whether each equation is a conditional equation or an ide...
 7.36: determine whether each equation is a conditional equation or an ide...
 7.37: determine whether each equation is a conditional equation or an ide...
 7.38: determine whether each equation is a conditional equation or an ide...
 7.39: determine whether each equation is a conditional equation or an ide...
 7.40: determine whether each equation is a conditional equation or an ide...
 7.41: determine whether each equation is a conditional equation or an ide...
 7.42: determine whether each equation is a conditional equation or an ide...
 7.43: determine whether each equation is a conditional equation or an ide...
 7.44: determine whether each equation is a conditional equation or an ide...
 7.45: determine whether each equation is a conditional equation or an ide...
 7.46: determine whether each equation is a conditional equation or an ide...
 7.47: determine whether each equation is a conditional equation or an ide...
 7.48: determine whether each equation is a conditional equation or an ide...
 7.49: determine whether each equation is a conditional equation or an ide...
 7.50: determine whether each equation is a conditional equation or an ide...
 7.51: determine whether each equation is a conditional equation or an ide...
 7.52: determine whether each equation is a conditional equation or an ide...
 7.53: graph each of the functions by rst rewriting it as a sine, cosine, ...
 7.54: graph each of the functions by rst rewriting it as a sine, cosine, ...
 7.55: graph each of the functions by rst rewriting it as a sine, cosine, ...
 7.56: graph each of the functions by rst rewriting it as a sine, cosine, ...
 7.57: graph each of the functions by rst rewriting it as a sine, cosine, ...
 7.58: graph each of the functions by rst rewriting it as a sine, cosine, ...
 7.59: graph each of the functions by rst rewriting it as a sine, cosine, ...
 7.60: graph each of the functions by rst rewriting it as a sine, cosine, ...
 7.61: graph each of the functions by rst rewriting it as a sine, cosine, ...
 7.62: graph each of the functions by rst rewriting it as a sine, cosine, ...
 7.63: refer to the following:The difference quotient, , is used to approx...
 7.64: refer to the following:The difference quotient, , is used to approx...
 7.65: use the following: A nonvertical line makes an angle with the xaxi...
 7.66: use the following: A nonvertical line makes an angle with the xaxi...
 7.67: refer to the following: An electric eld E of a wave with constant a...
 7.68: refer to the following: An electric eld E of a wave with constant a...
 7.69: Biology. By analyzing available empirical data, it has been determi...
 7.70: Health/Medicine. During the course of treatment of an illness, the ...
 7.71: explain the mistake that is made. Find the exact value of Solution:...
 7.72: explain the mistake that is made. Find the exact value of tan a7p 6...
 7.73: determine whether each statement is true or false.cos(15) = cos(45)...
 7.74: determine whether each statement is true or false. sin ap 2b = sin ...
 7.75: determine whether each statement is true or false.tanax +p 4b = 1 +...
 7.76: determine whether each statement is true or false.cot ap 4  xb =1 ...
 7.77: Verify that .
 7.78: Verify that .
 7.79: Although in general the statement is not true, it is true for some ...
 7.80: Although in general the statement is not true, it is true for some ...
 7.81: In Exercise 63, you showed that the difference quotient for is Plot...
 7.82: Show that the difference quotient for is Plot fora. b. c. What func...
 7.83: Show that the difference quotient for is.Plot fora. b. c. What func...
 7.84: Show that the difference quotient for is Plot fora. b. c. What func...
 7.1: use the doubleangle identities to answer the following questions.I...
 7.2: use the doubleangle identities to answer the following questions. ...
 7.3: use the doubleangle identities to answer the following questions. ...
 7.4: use the doubleangle identities to answer the following questions. ...
 7.5: use the doubleangle identities to answer the following questions. ...
 7.6: use the doubleangle identities to answer the following questions.I...
 7.7: use the doubleangle identities to answer the following questions.I...
 7.8: use the doubleangle identities to answer the following questions.I...
 7.9: use the doubleangle identities to answer the following questions.I...
 7.10: use the doubleangle identities to answer the following questions.I...
 7.11: use the doubleangle identities to answer the following questions.I...
 7.12: use the doubleangle identities to answer the following questions.I...
 7.13: simplify each expression. Evaluate the resulting expression exactly...
 7.14: simplify each expression. Evaluate the resulting expression exactly...
 7.15: simplify each expression. Evaluate the resulting expression exactly...
 7.16: simplify each expression. Evaluate the resulting expression exactly...
 7.17: simplify each expression. Evaluate the resulting expression exactly...
 7.18: simplify each expression. Evaluate the resulting expression exactly...
 7.19: simplify each expression. Evaluate the resulting expression exactly...
 7.20: simplify each expression. Evaluate the resulting expression exactly...
 7.21: simplify each expression. Evaluate the resulting expression exactly...
 7.22: simplify each expression. Evaluate the resulting expression exactly...
 7.23: simplify each expression. Evaluate the resulting expression exactly...
 7.24: simplify each expression. Evaluate the resulting expression exactly...
 7.25: verify each identity.
 7.26: verify each identity.cot(2A) = 1 2(cot A  tan A
 7.27: verify each identity.
 7.28: verify each identity.(sin x + cos x)2 = 1 + sin(2x
 7.29: verify each identity.
 7.30: verify each identity.sin2 x =1  cos(2x) 2
 7.31: verify each identity.
 7.32: verify each identity.cos4 x + sin4 x = 1  1 2 sin2 (2x
 7.33: verify each identity.
 7.34: verify each identity.[cos(2x)  sin(2x)][sin(2x) + cos(2x)] = cos(4x
 7.35: verify each identity.
 7.36: verify each identity.4 csc(4 x) =sec x csc x cos (2x)1
 7.37: verify each identity.
 7.38: verify each identity.tan(3x) =tan x (3  tan2 x) (1  3 tan2 x)
 7.39: verify each identity.
 7.40: verify each identity.cos(4 x) = [cos(2 x)  sin(2x)][(cos(2x) + sin...
 7.41: graph the functions.
 7.42: graph the functions.
 7.43: graph the functions.
 7.44: graph the functions.
 7.45: graph the functions.
 7.46: graph the functions.
 7.47: graph the functions.
 7.48: graph the functions.
 7.49: graph the functions.
 7.50: graph the functions.
 7.51: Business/Economics. Annual cash ow of a stock fund (measured as a p...
 7.52: Business. Computer sales are generally subject to seasonal uctuatio...
 7.53: refer to the following: An orecrusher wheel consists of a heavy di...
 7.54: refer to the following: An orecrusher wheel consists of a heavy di...
 7.55: With the information given in the diagram below, compute y.
 7.56: With the information given in the diagram below, compute x.
 7.57: explain the mistake that is made.f nd given Solution: Write the dou...
 7.58: explain the mistake that is made.If nd given Solution:Use the quoti...
 7.59: determine whether each statement is true or false.sin(2A) + sin(2A)...
 7.60: determine whether each statement is true or false.cos(4A)  cos(2A)...
 7.61: determine whether each statement is true or false.If then
 7.62: determine whether each statement is true or false. If then
 7.63: determine whether each statement is true or false. If then cos(2x) ...
 7.64: determine whether each statement is true or false. ifand only if th...
 7.65: determine whether each statement is true or false.cos2 (3x)  sin2 ...
 7.66: determine whether each statement is true or false.1  2 sin2 ax 2b ...
 7.67: determine whether each statement is true or false. is an even funct...
 7.68: Express in terms of functions of
 7.69: Express in terms of functions of tan x.
 7.70: Istheidentity truefor Explain
 7.71: Istheidentity true for Explain. x =
 7.72: One cannot prove that an equation is an identity using technology, ...
 7.73: One cannot prove that an equation is an identity using technology, ...
 7.74: One cannot prove that an equation is an identity using technology, ...
 7.75: One cannot prove that an equation is an identity using technology, ...
 7.76: One cannot prove that an equation is an identity using technology, ...
 7.77: One cannot prove that an equation is an identity using technology, ...
 7.1: use the halfangle identities to nd the exact values of the trigono...
 7.2: use the halfangle identities to nd the exact values of the trigono...
 7.3: use the halfangle identities to nd the exact values of the trigono...
 7.4: use the halfangle identities to nd the exact values of the trigono...
 7.5: use the halfangle identities to nd the exact values of the trigono...
 7.6: use the halfangle identities to nd the exact values of the trigono...
 7.7: use the halfangle identities to nd the exact values of the trigono...
 7.8: use the halfangle identities to nd the exact values of the trigono...
 7.9: use the halfangle identities to nd the exact values of the trigono...
 7.10: use the halfangle identities to nd the exact values of the trigono...
 7.11: use the halfangle identities to nd the exact values of the trigono...
 7.12: use the halfangle identities to nd the exact values of the trigono...
 7.13: use the halfangle identities to nd the exact values of the trigono...
 7.14: use the halfangle identities to nd the exact values of the trigono...
 7.15: use the halfangle identities to nd the exact values of the trigono...
 7.16: use the halfangle identities to nd the exact values of the trigono...
 7.17: use the halfangle identities to nd the desired function values.If ...
 7.18: use the halfangle identities to nd the desired function values.If ...
 7.19: use the halfangle identities to nd the desired function values.If ...
 7.20: use the halfangle identities to nd the desired function values.If ...
 7.21: use the halfangle identities to nd the desired function values.If ...
 7.22: use the halfangle identities to nd the desired function values.If ...
 7.23: use the halfangle identities to nd the desired function values.If ...
 7.24: use the halfangle identities to nd the desired function values.If ...
 7.25: use the halfangle identities to nd the desired function values.If ...
 7.26: use the halfangle identities to nd the desired function values.If ...
 7.27: use the halfangle identities to nd the desired function values.If ...
 7.28: use the halfangle identities to nd the desired function values.If ...
 7.29: use the halfangle identities to nd the desired function values.If ...
 7.30: use the halfangle identities to nd the desired function values.If ...
 7.31: use the halfangle identities to nd the desired function values.If ...
 7.32: use the halfangle identities to nd the desired function values.If ...
 7.33: simplify each expression using halfangle identities. Do not evaluate.
 7.34: simplify each expression using halfangle identities. Do not evaluate.
 7.35: simplify each expression using halfangle identities. Do not evaluate.
 7.36: simplify each expression using halfangle identities. Do not evaluate.
 7.37: simplify each expression using halfangle identities. Do not evaluate.
 7.38: simplify each expression using halfangle identities. Do not evaluate.
 7.39: verify the identities.
 7.40: verify the identities.
 7.41: verify the identities.
 7.42: verify the identities.
 7.43: verify the identities.
 7.44: verify the identities.
 7.45: verify the identities.
 7.46: verify the identities.
 7.47: verify the identities.
 7.48: verify the identities.
 7.49: verify the identities.
 7.50: verify the identities.
 7.51: graph the functions.
 7.52: graph the functions.
 7.53: graph the functions.
 7.54: graph the functions.
 7.55: graph the functions.
 7.56: graph the functions.
 7.57: graph the functions.
 7.58: graph the functions.
 7.59: Business. If monthly prots are $3000 and monthly sales are $4000, n...
 7.60: Business. If monthly prots are p and monthly sales are s (where p s...
 7.61: Area of an Isosceles Triangle. Consider the triangle below, where t...
 7.62: Area of an Isosceles Triangle. Consider the triangle below, where t...
 7.63: explain the mistake that is made.explain the mistake that is made.
 7.64: explain the mistake that is made. If , nd .Solution:Use the quotien...
 7.65: determine whether each statement is true or false.
 7.66: determine whether each statement is true or false.cosaA 2b + cosaA ...
 7.67: determine whether each statement is true or false.
 7.68: determine whether each statement is true or false.If then sinax 2 b...
 7.69: determine whether each statement is true or false.
 7.70: Given verify Substitute into the identity and explain your results.
 7.71: Prove that .
 7.72: Prove that cotaA 2 b secaA 2bcscaA 2btanaA 2 b = 2 csc A.
 7.73: Find the values of x in the interval for which
 7.74: Find the values of x in the interval for which cota x 2 b 0.
 7.75: One cannot prove that an equation is an identity using technology, ...
 7.76: One cannot prove that an equation is an identity using technology, ...
 7.77: One cannot prove that an equation is an identity using technology, ...
 7.78: One cannot prove that an equation is an identity using technology, ...
 7.79: One cannot prove that an equation is an identity using technology, ...
 7.80: One cannot prove that an equation is an identity using technology, ...
 7.1: write each product as a sum or difference of sines and/or cosines.
 7.2: write each product as a sum or difference of sines and/or cosines.
 7.3: write each product as a sum or difference of sines and/or cosines.
 7.4: write each product as a sum or difference of sines and/or cosines.
 7.5: write each product as a sum or difference of sines and/or cosines.
 7.6: write each product as a sum or difference of sines and/or cosines.
 7.7: write each product as a sum or difference of sines and/or cosines.
 7.8: write each product as a sum or difference of sines and/or cosines.
 7.9: write each product as a sum or difference of sines and/or cosines.
 7.10: write each product as a sum or difference of sines and/or cosines.
 7.11: write each product as a sum or difference of sines and/or cosines.
 7.12: write each product as a sum or difference of sines and/or cosines.
 7.13: write each product as a sum or difference of sines and/or cosines.
 7.14: write each product as a sum or difference of sines and/or cosines.
 7.15: write each expression as a product of sines and/or cosines.
 7.16: write each expression as a product of sines and/or cosines.
 7.17: write each expression as a product of sines and/or cosines.
 7.18: write each expression as a product of sines and/or cosines.
 7.19: write each expression as a product of sines and/or cosines.
 7.20: write each expression as a product of sines and/or cosines.
 7.21: write each expression as a product of sines and/or cosines.
 7.22: write each expression as a product of sines and/or cosines.
 7.23: write each expression as a product of sines and/or cosines.
 7.24: write each expression as a product of sines and/or cosines.
 7.25: write each expression as a product of sines and/or cosines.
 7.26: write each expression as a product of sines and/or cosines.
 7.27: write each expression as a product of sines and/or cosines.
 7.28: write each expression as a product of sines and/or cosines.
 7.29: simplify the trigonometric expressions.
 7.30: simplify the trigonometric expressions.
 7.31: simplify the trigonometric expressions.os x  cos(3x) sin(3x)  sin x
 7.32: simplify the trigonometric expressions.in(7x)  sin(2x) cos(7x)  c...
 7.33: simplify the trigonometric expressions.
 7.34: simplify the trigonometric expressions.
 7.35: verify the identities.
 7.36: verify the identities.Business. An analysis of the monthly costs an...
 7.37: verify the identities.
 7.38: verify the identities.
 7.39: verify the identities.
 7.40: verify the identities.
 7.41: verify the identities.
 7.42: verify the identities.
 7.43: Business. An analysis of the monthly costs and monthly revenues of ...
 7.44: Business. An analysis of the monthly costs and monthly revenues of ...
 7.45: Music. Write a mathematical description of a tone that results from...
 7.46: Music.Write a mathematical description of a tone that results from ...
 7.47: Optics.Two optical signals with uniform intensities and wavelengths...
 7.48: Optics. The two optical signals in Exercise 47 are beat together. W...
 7.49: Touchtone keypads have the following simultaneous low and high fre...
 7.50: Touchtone keypads have the following simultaneous low and high fre...
 7.51: Area of a Triangle.A formula for nding the area of a triangle when ...
 7.52: Area of a Triangle. If the measures of angles B and C in Exercise 5...
 7.53: explain the mistake that is made. Simplify the expression Solution:...
 7.54: explain the mistake that is made. Simplify the expression Solution:...
 7.55: determine whether each statement is true or false.
 7.56: determine whether each statement is true or false.
 7.57: determine whether each statement is true or false. The product of t...
 7.58: determine whether each statement is true or false. The product of t...
 7.59: determine whether each statement is true or false. Write as a sum o...
 7.60: determine whether each statement is true or false. Write as a sum o...
 7.61: Prove the addition formula using the identities of this section.
 7.62: Prove the difference formulausing the identities of this section.
 7.63: Graph y = 1  3 sin(x) sin a 6 xb.
 7.64: Graph y = 4 sin(2x  1) cos(2  x).
 7.65: Graph y = cosa2 3 xb cosa5 6 xb.
 7.66: Graph y = x  cos(2x) sin(3x).
 7.67: Suggest an identity by graphing and determining the function based ...
 7.68: Suggest an identity by graphing and determining the function based ...
 7.69: With a graphing calculator, plot and in the same Y3 = 1 2 [cos(2x) ...
 7.70: With a graphing calculator, plot and in the same Y3 = 1 2 [cos(6x) ...
 7.1: nd the exact value of each expression. Give the answer in radians.
 7.6: nd the exact value of each expression. Give the answer in radians.
 7.7: nd the exact value of each expression. Give the answer in radians.
 7.8: nd the exact value of each expression. Give the answer in radians.
 7.9: nd the exact value of each expression. Give the answer in radians.
 7.10: nd the exact value of each expression. Give the answer in radians.
 7.11: nd the exact value of each expression. Give the answer in radians.
 7.12: nd the exact value of each expression. Give the answer in radians.
 7.13: nd the exact value of each expression. Give the answer in radians.
 7.14: nd the exact value of each expression. Give the answer in radians.
 7.15: nd the exact value of each expression. Give the answer in radians.
 7.16: nd the exact value of each expression. Give the answer in radians.
 7.17: nd the exact value of each expression. Give the answer in degrees.
 7.18: nd the exact value of each expression. Give the answer in degrees.
 7.19: nd the exact value of each expression. Give the answer in degrees.
 7.20: nd the exact value of each expression. Give the answer in degrees.
 7.21: nd the exact value of each expression. Give the answer in degrees.
 7.22: nd the exact value of each expression. Give the answer in degrees.
 7.23: nd the exact value of each expression. Give the answer in degrees.
 7.24: nd the exact value of each expression. Give the answer in degrees.
 7.25: nd the exact value of each expression. Give the answer in degrees.
 7.26: nd the exact value of each expression. Give the answer in degrees.
 7.27: nd the exact value of each expression. Give the answer in degrees.
 7.28: nd the exact value of each expression. Give the answer in degrees.
 7.29: nd the exact value of each expression. Give the answer in degrees.
 7.30: nd the exact value of each expression. Give the answer in degrees.
 7.31: nd the exact value of each expression. Give the answer in degrees.
 7.32: nd the exact value of each expression. Give the answer in degrees.
 7.33: , use a calculator to evaluate each expression. Give the answer in ...
 7.34: , use a calculator to evaluate each expression. Give the answer in ...
 7.35: , use a calculator to evaluate each expression. Give the answer in ...
 7.36: , use a calculator to evaluate each expression. Give the answer in ...
 7.37: , use a calculator to evaluate each expression. Give the answer in ...
 7.38: , use a calculator to evaluate each expression. Give the answer in ...
 7.39: , use a calculator to evaluate each expression. Give the answer in ...
 7.40: , use a calculator to evaluate each expression. Give the answer in ...
 7.41: , use a calculator to evaluate each expression. Give the answer in ...
 7.42: , use a calculator to evaluate each expression. Give the answer in ...
 7.43: use a calculator to evaluate each expression. Give the answer in ra...
 7.44: use a calculator to evaluate each expression. Give the answer in ra...
 7.45: use a calculator to evaluate each expression. Give the answer in ra...
 7.46: use a calculator to evaluate each expression. Give the answer in ra...
 7.47: use a calculator to evaluate each expression. Give the answer in ra...
 7.48: use a calculator to evaluate each expression. Give the answer in ra...
 7.49: use a calculator to evaluate each expression. Give the answer in ra...
 7.50: use a calculator to evaluate each expression. Give the answer in ra...
 7.51: use a calculator to evaluate each expression. Give the answer in ra...
 7.52: use a calculator to evaluate each expression. Give the answer in ra...
 7.53: evaluate each expression exactly, if possible. If not possible, sta...
 7.54: evaluate each expression exactly, if possible. If not possible, sta...
 7.55: evaluate each expression exactly, if possible. If not possible, sta...
 7.56: evaluate each expression exactly, if possible. If not possible, sta...
 7.57: evaluate each expression exactly, if possible. If not possible, sta...
 7.58: evaluate each expression exactly, if possible. If not possible, sta...
 7.59: evaluate each expression exactly, if possible. If not possible, sta...
 7.60: evaluate each expression exactly, if possible. If not possible, sta...
 7.61: evaluate each expression exactly, if possible. If not possible, sta...
 7.62: evaluate each expression exactly, if possible. If not possible, sta...
 7.63: evaluate each expression exactly, if possible. If not possible, sta...
 7.64: evaluate each expression exactly, if possible. If not possible, sta...
 7.65: evaluate each expression exactly, if possible. If not possible, sta...
 7.66: evaluate each expression exactly, if possible. If not possible, sta...
 7.67: evaluate each expression exactly, if possible. If not possible, sta...
 7.68: evaluate each expression exactly, if possible. If not possible, sta...
 7.69: evaluate each expression exactly, if possible. If not possible, sta...
 7.70: evaluate each expression exactly, if possible. If not possible, sta...
 7.71: evaluate each expression exactly, if possible. If not possible, sta...
 7.72: evaluate each expression exactly, if possible. If not possible, sta...
 7.73: evaluate each expression exactly, if possible. If not possible, sta...
 7.74: evaluate each expression exactly, if possible. If not possible, sta...
 7.75: evaluate each expression exactly, if possible. If not possible, sta...
 7.76: evaluate each expression exactly, if possible. If not possible, sta...
 7.77: evaluate each expression exactly.
 7.78: evaluate each expression exactly.
 7.79: evaluate each expression exactly.
 7.80: evaluate each expression exactly.
 7.81: evaluate each expression exactly.
 7.82: evaluate each expression exactly.
 7.83: evaluate each expression exactly.
 7.84: evaluate each expression exactly.
 7.85: evaluate each expression exactly.
 7.86: evaluate each expression exactly.
 7.87: evaluate each expression exactly.
 7.88: evaluate each expression exactly.
 7.89: evaluate each expression exactly.
 7.90: evaluate each expression exactly.
 7.91: evaluate each expression exactly.
 7.92: evaluate each expression exactly.
 7.93: evaluate each expression exactly.
 7.94: evaluate each expression exactly.
 7.95: evaluate each expression exactly.
 7.96: evaluate each expression exactly.
 7.97: For each of the following expressions, write an equivalent expressi...
 7.98: For each of the following expressions, write an equivalent expressi...
 7.99: For each of the following expressions, write an equivalent expressi...
 7.100: For each of the following expressions, write an equivalent expressi...
 7.101: refer to the following: Annual sales of a product are generally sub...
 7.102: refer to the following: Annual sales of a product are generally sub...
 7.103: refer to the following: Allergy sufferers symptoms uctuate with pol...
 7.104: refer to the following: Allergy sufferers symptoms uctuate with pol...
 7.105: Alternating Current. Alternating electrical current in amperes (A) ...
 7.106: Alternating Current. If the frequency is 100 Hz and maximum current...
 7.107: Hours of Daylight. The number of hours of daylight in San Diego, Ca...
 7.108: Hours of Daylight. Repeat Exercise 107. For what value of t is the ...
 7.109: Money. A young couple get married and immediately start saving mone...
 7.110: Money. For the couple in Exercise 109, how many years into their ma...
 7.111: Viewing Angle of Painting. A museum patron whose eye level is 5 fee...
 7.112: Viewing Angle of Painting. Using the equation for in Exercise 111, ...
 7.113: Earthquake Movement. The horizontal movement of a point that is k k...
 7.114: Earthquake Movement. Repeat Exercise 113. If an earthquake produces...
 7.115: Laser Communication. A laser communication system depends on a narr...
 7.116: Laser Communication. Repeat Exercise 115, assuming that the ground ...
 7.117: explain the mistake that is made.Evaluate the expression exactly: ....
 7.118: explain the mistake that is made.Evaluate the expression exactly: S...
 7.119: explain the mistake that is made.Evaluate the expression exactly: S...
 7.120: explain the mistake that is made.Evaluate the expression exactly:So...
 7.121: determine whether each statement is true or false.The inverse secan...
 7.122: determine whether each statement is true or false.The inverse cosec...
 7.123: determine whether each statement is true or false. for all in the d...
 7.124: determine whether each statement is true or false. for all for whic...
 7.125: Explain why does not exist.
 7.126: Explain why does not exist.
 7.127: Find the expression that corresponds to .
 7.128: Determine the xvalues for which
 7.129: Evaluate exactly:
 7.130: Let a. State an accepted domain of f(x) so that f(x) is a onetoone...
 7.131: Let a. State an accepted domain of f(x) so that f(x) is a onetoone...
 7.132: Let a. State an accepted domain of f(x) so that f(x) is a onetoone...
 7.133: Let a. State an accepted domain of f(x) so that f(x) is a onetoone...
 7.134: Let a. State an accepted domain of f(x) so that f(x) is a onetoone...
 7.135: Use a graphing calculator to plot and for the domain If you then in...
 7.136: Use a graphing calculator to plot and for the domain If you then in...
 7.137: Use a graphing calculator to plot and Determine the domain for whic...
 7.138: Use a graphing calculator to plot and Determine the domain for whic...
 7.139: Given a. Find sin(2x) using the doubleangle identity. b. Use the i...
 7.140: Given a. Find tan(2x) using the doubleangle identity. b. Use the i...
 7.1: solve the given trigonometric equation exactly over the indicated i...
 7.2: solve the given trigonometric equation exactly over the indicated i...
 7.3: solve the given trigonometric equation exactly over the indicated i...
 7.4: solve the given trigonometric equation exactly over the indicated i...
 7.5: solve the given trigonometric equation exactly over the indicated i...
 7.6: solve the given trigonometric equation exactly over the indicated i...
 7.7: solve the given trigonometric equation exactly over the indicated i...
 7.8: solve the given trigonometric equation exactly over the indicated i...
 7.9: solve the given trigonometric equation exactly over the indicated i...
 7.10: solve the given trigonometric equation exactly over the indicated i...
 7.11: solve the given trigonometric equation exactly over the indicated i...
 7.12: solve the given trigonometric equation exactly over the indicated i...
 7.13: solve the given trigonometric equation exactly over the indicated i...
 7.14: solve the given trigonometric equation exactly over the indicated i...
 7.15: solve the given trigonometric equation exactly over the indicated i...
 7.16: solve the given trigonometric equation exactly over the indicated i...
 7.17: solve the given trigonometric equation exactly over the indicated i...
 7.18: solve the given trigonometric equation exactly over the indicated i...
 7.19: solve the given trigonometric equation exactly over the indicated i...
 7.20: solve the given trigonometric equation exactly over the indicated i...
 7.21: solve the given trigonometric equation exactly on 0 2.
 7.22: solve the given trigonometric equation exactly on 0 2.
 7.23: solve the given trigonometric equation exactly on 0 2.
 7.24: solve the given trigonometric equation exactly on 0 2.
 7.25: solve the given trigonometric equation exactly on 0 2.
 7.26: solve the given trigonometric equation exactly on 0 2.
 7.27: solve the given trigonometric equation exactly on 0 2.
 7.28: solve the given trigonometric equation exactly on 0 2.
 7.29: solve the given trigonometric equation exactly on 0 2.
 7.30: solve the given trigonometric equation exactly on 0 2.
 7.31: solve the given trigonometric equation exactly on 0 2.
 7.32: solve the given trigonometric equation exactly on 0 2.
 7.33: solve the given trigonometric equation exactly on 0 2.
 7.34: solve the given trigonometric equation exactly on 0 2.
 7.35: solve the given trigonometric equation exactly on 0 2.
 7.36: solve the given trigonometric equation exactly on 0 2.
 7.37: solve the given trigonometric equation exactly on 0 2.
 7.38: solve the given trigonometric equation exactly on 0 2.
 7.39: solve the given trigonometric equation exactly on 0 2.
 7.40: solve the given trigonometric equation exactly on 0 2.
 7.41: solve the given trigonometric equation on 0 360 and express the ans...
 7.42: solve the given trigonometric equation on 0 360 and express the ans...
 7.43: solve the given trigonometric equation on 0 360 and express the ans...
 7.44: solve the given trigonometric equation on 0 360 and express the ans...
 7.45: solve the given trigonometric equation on 0 360 and express the ans...
 7.46: solve the given trigonometric equation on 0 360 and express the ans...
 7.47: solve the given trigonometric equation on 0 360 and express the ans...
 7.48: solve the given trigonometric equation on 0 360 and express the ans...
 7.49: solve the given trigonometric equation on 0 360 and express the ans...
 7.50: solve the given trigonometric equation on 0 360 and express the ans...
 7.51: solve the given trigonometric equation on 0 360 and express the ans...
 7.52: solve the given trigonometric equation on 0 360 and express the ans...
 7.53: solve the given trigonometric equation on 0 360 and express the ans...
 7.54: solve the given trigonometric equation on 0 360 and express the ans...
 7.55: solve the given trigonometric equation on 0 360 and express the ans...
 7.56: solve the given trigonometric equation on 0 360 and express the ans...
 7.57: solve the given trigonometric equation on 0 360 and express the ans...
 7.58: solve the given trigonometric equation on 0 360 and express the ans...
 7.59: solve the given trigonometric equation on 0 360 and express the ans...
 7.60: solve the given trigonometric equation on 0 360 and express the ans...
 7.61: solve the trigonometric equations exactly on the indicated interval...
 7.62: solve the trigonometric equations exactly on the indicated interval...
 7.63: solve the trigonometric equations exactly on the indicated interval...
 7.64: solve the trigonometric equations exactly on the indicated interval...
 7.65: solve the trigonometric equations exactly on the indicated interval...
 7.66: solve the trigonometric equations exactly on the indicated interval...
 7.67: solve the trigonometric equations exactly on the indicated interval...
 7.68: solve the trigonometric equations exactly on the indicated interval...
 7.69: solve the trigonometric equations exactly on the indicated interval...
 7.70: solve the trigonometric equations exactly on the indicated interval...
 7.71: solve the trigonometric equations exactly on the indicated interval...
 7.72: solve the trigonometric equations exactly on the indicated interval...
 7.73: solve the trigonometric equations exactly on the indicated interval...
 7.74: solve the trigonometric equations exactly on the indicated interval...
 7.75: solve the trigonometric equations exactly on the indicated interval...
 7.76: solve the trigonometric equations exactly on the indicated interval...
 7.77: solve the trigonometric equations exactly on the indicated interval...
 7.78: solve the trigonometric equations exactly on the indicated interval...
 7.79: solve the trigonometric equations exactly on the indicated interval...
 7.80: solve the trigonometric equations exactly on the indicated interval...
 7.81: solve the trigonometric equations exactly on the indicated interval...
 7.82: solve the trigonometric equations exactly on the indicated interval...
 7.83: solve the trigonometric equations exactly on the indicated interval...
 7.84: solve the trigonometric equations exactly on the indicated interval...
 7.85: solve the trigonometric equations exactly on the indicated interval...
 7.86: solve the trigonometric equations exactly on the indicated interval...
 7.87: solve the trigonometric equations exactly on the indicated interval...
 7.88: solve the trigonometric equations exactly on the indicated interval...
 7.89: solve each trigonometric equation on 0 360 . Express solutions in d...
 7.90: solve each trigonometric equation on 0 360 . Express solutions in d...
 7.91: solve each trigonometric equation on 0 360 . Express solutions in d...
 7.92: solve each trigonometric equation on 0 360 . Express solutions in d...
 7.93: solve each trigonometric equation on 0 360 . Express solutions in d...
 7.94: solve each trigonometric equation on 0 360 . Express solutions in d...
 7.95: solve each trigonometric equation on 0 360 . Express solutions in d...
 7.96: solve each trigonometric equation on 0 360 . Express solutions in d...
 7.97: solve each trigonometric equation on 0 360 . Express solutions in d...
 7.98: solve each trigonometric equation on 0 360 . Express solutions in d...
 7.99: refer to the following: Computer sales are generally subject to sea...
 7.100: refer to the following: Computer sales are generally subject to sea...
 7.101: refer to the following: Allergy sufferers symptoms uctuate with the...
 7.102: refer to the following: Allergy sufferers symptoms uctuate with the...
 7.103: Sales. Monthly sales of soccer balls are approximated by where x is...
 7.104: Sales. Monthly sales of soccer balls are approximated bywhere x is ...
 7.105: Home Improvement. A rain gutter is constructed from a single strip ...
 7.106: Home Improvement. A rain gutter is constructed from a single strip ...
 7.107: Deer Population. The number of deer on an island is givenby where x...
 7.108: Deer Population. The number of deer on an island is givenby where x...
 7.109: Optics. Assume that light is going from air into a diamond. Calcula...
 7.110: Optics. Assume that light is going from a diamond into air. Calcula...
 7.111: Air in Lungs. If a person breathes in and out every 3 seconds, the ...
 7.112: Air in Lungs. For the function given in Exercise 111, how many seco...
 7.113: refer to the following: The gure below shows the graph of between T...
 7.114: refer to the following: The gure below shows the graph of between T...
 7.115: Business. An analysis of a companys costs and revenue shows that an...
 7.116: Business. An analysis of a companys costs and revenue shows that th...
 7.117: refer to the following: By analyzing available empirical data, it h...
 7.118: refer to the following: By analyzing available empirical data, it h...
 7.119: explain the mistake that is made. Solve on . Solution: Square both ...
 7.120: explain the mistake that is made. Solve on . Solution: Square both ...
 7.121: explain the mistake that is made. Solve on Solution: Use the double...
 7.122: explain the mistake that is made. Solve on Solution: Square both si...
 7.123: Linear trigonometric equations always have one solution
 7.124: determine whether each statement is true or false.Quadratic trigono...
 7.125: determine whether each statement is true or false.If a trigonometri...
 7.126: determine whether each statement is true or false.If a trigonometri...
 7.127: Solve over
 7.128: Solve over all real numbers.
 7.129: Solve for the smallest positive x that makes this statement true:
 7.130: Solve for the smallest positive x that makes this statement true: c...
 7.131: Find all real numbers x such that
 7.132: Find all real numbers such that
 7.133: Find all real numbers such that
 7.134: Find all real numbers x such that
 7.135: Graphing calculators can be used to nd approximate solutions to tri...
 7.136: Graphing calculators can be used to nd approximate solutions to tri...
 7.137: Graphing calculators can be used to nd approximate solutions to tri...
 7.138: Graphing calculators can be used to nd approximate solutions to tri...
 7.139: Graphing calculators can be used to nd approximate solutions to tri...
 7.140: Graphing calculators can be used to nd approximate solutions to tri...
 7.141: Find the smallest positive values of x that make the statement true...
 7.142: Find the smallest positive values of x that make the statement true...
 7.143: Find the smallest positive values of x that make the statement true...
 7.144: Find the smallest positive values of x that make the statement true...
 7.145: Find the smallest positive values of x that make the statement true...
 7.146: Find the smallest positive values of x that make the statement true...
 7.1: Use trigonometric identities to nd the indicated value(s).
 7.2: Use trigonometric identities to nd the indicated value(s).
 7.3: Use trigonometric identities to nd the indicated value(s).
 7.4: Use trigonometric identities to nd the indicated value(s).
 7.5: Use trigonometric identities to nd the indicated value(s).
 7.6: Use trigonometric identities to nd the indicated value(s).
 7.7: Use trigonometric identities to nd the indicated value(s).
 7.8: Use trigonometric identities to nd the indicated value(s).
 7.9: Use trigonometric identities to nd the indicated value(s).
 7.10: Use trigonometric identities to nd the indicated value(s).
 7.11: Use trigonometric identities to nd the indicated value(s).
 7.12: Use trigonometric identities to nd the indicated value(s).
 7.13: Use trigonometric identities to nd the indicated value(s).
 7.14: Use trigonometric identities to nd the indicated value(s).
 7.15: Perform the operations and simplify. Write the answers in terms of and
 7.16: Perform the operations and simplify. Write the answers in terms of and
 7.17: Perform the operations and simplify. Write the answers in terms of and
 7.18: Perform the operations and simplify. Write the answers in terms of and
 7.19: Perform the operations and simplify. Write the answers in terms of and
 7.20: Perform the operations and simplify. Write the answers in terms of and
 7.21: Simplify the following trigonometric expressions.
 7.22: Simplify the following trigonometric expressions.
 7.23: Simplify the following trigonometric expressions.
 7.24: Simplify the following trigonometric expressions.
 7.25: Simplify the following trigonometric expressions.
 7.26: Simplify the following trigonometric expressions.
 7.27: Simplify the following trigonometric expressions.
 7.28: Simplify the following trigonometric expressions.
 7.29: Verify the trigonometric identities. (tanx + cotx)2  2 = tan2x + c...
 7.30: Verify the trigonometric identities. csc2x  cot2x = 1
 7.31: Verify the trigonometric identities. in2x 1 tan2x = 1
 7.32: Verify the trigonometric identities. 1 cscx + 1+1 cscx  1=2tanx cosx
 7.33: Verify the trigonometric identities. tan2x  1 sec2x + 3tanx + 1=ta...
 7.34: Verify the trigonometric identities. cotx(secx  cosx) = sinx
 7.35: Determine whether each of the following equations is a conditional ...
 7.36: Determine whether each of the following equations is a conditional ...
 7.37: Determine whether each of the following equations is a conditional ...
 7.38: Determine whether each of the following equations is a conditional ...
 7.39: Determine whether each of the following equations is a conditional ...
 7.40: Determine whether each of the following equations is a conditional ...
 7.41: Find the exact value for each trigonometric expression.
 7.42: Find the exact value for each trigonometric expression.
 7.43: Find the exact value for each trigonometric expression.
 7.44: Find the exact value for each trigonometric expression.
 7.45: Write each expression as a single trigonometric function. sin(4x)co...
 7.46: Write each expression as a single trigonometric function. sin(x)si...
 7.47: Write each expression as a single trigonometric function. tan(5x) ...
 7.48: Write each expression as a single trigonometric function. tanap 4b ...
 7.49: Find the exact value of the indicated expression using the given in...
 7.50: Find the exact value of the indicated expression using the given in...
 7.51: Find the exact value of the indicated expression using the given in...
 7.52: Find the exact value of the indicated expression using the given in...
 7.53: Determine whether each of the following equations is a conditional ...
 7.54: Determine whether each of the following equations is a conditional ...
 7.55: Graph the following functions.y = cosap 2bcosx  sinap 2bsinx
 7.56: Graph the following functions.y = sina2p 3bcosx + cosa2p 3bsinx
 7.57: Graph the following functions.y =2tanax 3b1  tan2ax 3b
 7.58: Graph the following functions.y =tan(px)  tanx 1 + tan(px)tanx
 7.59: Use doubleangle identities to answer the following questions.If an...
 7.60: Use doubleangle identities to answer the following questions. If a...
 7.61: Use doubleangle identities to answer the following questions. If a...
 7.62: Use doubleangle identities to answer the following questions.If an...
 7.63: Use doubleangle identities to answer the following questions.If an...
 7.64: Use doubleangle identities to answer the following questions.If an...
 7.65: Simplify each of the following expressions. Evaluate exactly, if po...
 7.66: Simplify each of the following expressions. Evaluate exactly, if po...
 7.67: Simplify each of the following expressions. Evaluate exactly, if po...
 7.68: Simplify each of the following expressions. Evaluate exactly, if po...
 7.69: Verify the following identities.sin3A  cos3A = (sinA  cosA)C1 + 1...
 7.70: Verify the following identities.2sinAcos3A  2sin3AcosA = cos(2A)si...
 7.71: Verify the following identities.tanA =sin(2A) 1 + cos(2A)
 7.72: Verify the following identities.anA =1  cos(2A) sin(2A)
 7.73: Verify the following identities.Launching a Missile.When launching ...
 7.74: Verify the following identities.Launching a Missile.When launching ...
 7.75: Use halfangle identities to nd the exact value of each of the foll...
 7.76: Use halfangle identities to nd the exact value of each of the foll...
 7.77: Use halfangle identities to nd the exact value of each of the foll...
 7.78: Use halfangle identities to nd the exact value of each of the foll...
 7.79: Use halfangle identities to nd the exact value of each of the foll...
 7.80: Use halfangle identities to nd the exact value of each of the foll...
 7.81: Use halfangle identities to nd each of the following values.
 7.82: Use halfangle identities to nd each of the following values.
 7.83: Use halfangle identities to nd each of the following values.
 7.84: Use halfangle identities to nd each of the following values.
 7.85: Simplify each expression using halfangle identities. Do not evaluate.
 7.86: Simplify each expression using halfangle identities. Do not evaluate.
 7.87: Verify each of the following identities.csinaA 2b + cosaA 2b d2= 1 ...
 7.88: Verify each of the following identities.sec2aA 2b + tan2aA 2b =3  ...
 7.89: Verify each of the following identities.csc2aA 2b + cot2aA 2b =3 + ...
 7.90: Verify each of the following identities.tan2a A 2b + 1 = sec2a A 2b
 7.91: Graph each of the following functions.
 7.92: Graph each of the following functions.
 7.93: Graph each of the following functions.
 7.94: Graph each of the following functions.
 7.95: Write each product as a sum or difference of sines and/or cosines.
 7.96: Write each product as a sum or difference of sines and/or cosines.
 7.97: Write each expression as a product of sines and/or cosines.
 7.98: Write each expression as a product of sines and/or cosines.
 7.99: Write each expression as a product of sines and/or cosines.
 7.100: Write each expression as a product of sines and/or cosines.
 7.101: Simplify each trigonometric expression.
 7.102: Simplify each trigonometric expression.
 7.103: Verify the identities.
 7.104: Verify the identities.
 7.105: Verify the identities.
 7.106: Verify the identities.
 7.107: Find the exact value of each expression. Give the answer in radians...
 7.108: Find the exact value of each expression. Give the answer in radians...
 7.109: Find the exact value of each expression. Give the answer in radians.
 7.110: Find the exact value of each expression. Give the answer in radians.
 7.111: Find the exact value of each expression. Give the answer in radians.
 7.112: Find the exact value of each expression. Give the answer in radians.
 7.113: Find the exact value of each expression. Give the answer in degrees.
 7.114: Find the exact value of each expression. Give the answer in degrees.
 7.115: Find the exact value of each expression. Give the answer in degrees.
 7.116: Find the exact value of each expression. Give the answer in degrees.
 7.117: Find the exact value of each expression. Give the answer in degrees.
 7.118: Find the exact value of each expression. Give the answer in degrees.
 7.119: Use a calculator to evaluate each expression. Give the answer in de...
 7.120: Use a calculator to evaluate each expression. Give the answer in de...
 7.121: Use a calculator to evaluate each expression. Give the answer in de...
 7.122: Use a calculator to evaluate each expression. Give the answer in de...
 7.123: Use a calculator to evaluate each expression. Give the answer in ra...
 7.124: Use a calculator to evaluate each expression. Give the answer in ra...
 7.125: Use a calculator to evaluate each expression. Give the answer in ra...
 7.126: Use a calculator to evaluate each expression. Give the answer in ra...
 7.127: Evaluate each expression exactly, if possible. If not possible, sta...
 7.128: Evaluate each expression exactly, if possible. If not possible, sta...
 7.129: Evaluate each expression exactly, if possible. If not possible, sta...
 7.130: Evaluate each expression exactly, if possible. If not possible, sta...
 7.131: Evaluate each expression exactly, if possible. If not possible, sta...
 7.132: Evaluate each expression exactly, if possible. If not possible, sta...
 7.133: Evaluate each expression exactly.
 7.134: Evaluate each expression exactly.
 7.135: Evaluate each expression exactly.
 7.136: Evaluate each expression exactly.
 7.137: Evaluate each expression exactly.
 7.138: Evaluate each expression exactly.
 7.139: Average Temperature. If the average temperature in degrees in Chica...
 7.140: Average Temperature. If the average temperature in degrees in Chica...
 7.141: Solve the given trigonometric equation over the indicated interval.
 7.142: Solve the given trigonometric equation over the indicated interval.
 7.143: Solve the given trigonometric equation over the indicated interval.
 7.144: Solve the given trigonometric equation over the indicated interval.
 7.145: Solve the given trigonometric equation over the indicated interval.
 7.146: Solve the given trigonometric equation over the indicated interval.
 7.147: Solve each trigonometric equation exactly on 0 2.
 7.148: Solve each trigonometric equation exactly on 0 2.
 7.149: Solve each trigonometric equation exactly on 0 2.
 7.150: Solve each trigonometric equation exactly on 0 2.
 7.151: Solve each trigonometric equation exactly on 0 2.
 7.152: Solve each trigonometric equation exactly on 0 2.
 7.153: Solve the given trigonometric equations on 0 360 and express the an...
 7.154: Solve the given trigonometric equations on 0 360 and express the an...
 7.155: Solve the given trigonometric equations on 0 360 and express the an...
 7.156: Solve the given trigonometric equations on 0 360 and express the an...
 7.157: Solve the given trigonometric equations on 0 360 and express the an...
 7.158: Solve the given trigonometric equations on 0 360 and express the an...
 7.159: Solve each trigonometric equation exactly on the interval 0 2.
 7.160: Solve each trigonometric equation exactly on the interval 0 2.
 7.161: Solve each trigonometric equation exactly on the interval 0 2.
 7.162: Solve each trigonometric equation exactly on the interval 0 2.
 7.163: Solve each trigonometric equation exactly on the interval 0 2.
 7.164: Solve each trigonometric equation exactly on the interval 0 2.
 7.165: Solve each trigonometric equation exactly on the interval 0 2.
 7.166: Solve each trigonometric equation exactly on the interval 0 2.
 7.167: Solve each trigonometric equation exactly on the interval 0 2.
 7.168: Solve each trigonometric equation exactly on the interval 0 2.
 7.169: Solve each trigonometric equation exactly on the interval 0 2.
 7.170: Solve each trigonometric equation exactly on the interval 0 2.
 7.171: Solve each trigonometric equation on 0 360 . Give the answers in de...
 7.172: Solve each trigonometric equation on 0 360 . Give the answers in de...
 7.173: Solve each trigonometric equation on 0 360 . Give the answers in de...
 7.174: Solve each trigonometric equation on 0 360 . Give the answers in de...
 7.175: Solve each trigonometric equation on 0 360 . Give the answers in de...
 7.176: Solve each trigonometric equation on 0 360 . Give the answers in de...
 7.177: Is Use a calculator to nd each of the following: a. b. c. Which res...
 7.178: Is Use a calculator to nd each of the following. a. b. c. Which res...
 7.179: Determine the correct sign for by graphing and in the same viewing ...
 7.180: Determine the correct sign forbygraphing and in the same viewing re...
 7.181: Recall that the difference quotient for a function fis given by . S...
 7.182: Recall that the difference quotient for a function fis given by .Sh...
 7.183: Recall that the difference quotient for a function fis given by .Wi...
 7.184: Recall that the difference quotient for a function fis given by .Wi...
 7.185: With a graphing calculator, plot and in the same viewing rectangleb...
 7.186: With a graphing calculator, plot and in the same viewing rectangleb...
 7.187: With a graphing calculator, plot and in the same viewing rectangle ...
 7.188: With a graphing calculator, plot and in the same viewing rectangle ...
 7.189: Given a. Find cos(2x) using the doubleangle identity. b. Use the i...
 7.190: Given a. Find using the halfangle identity. b. Use the inverse of ...
 7.191: Find the smallest positive value of x that makes each statement tru...
 7.192: Find the smallest positive value of x that makes each statement tru...
 7.1: For what values of x does the quotient identitynot hold?
 7.2: Is the equation a conditional equation or an identity?
 7.3: Evaluate exactly.
 7.4: Evaluate exactly.
 7.5: If and nd
 7.6: If and nd
 7.7: Write as a cosine or sine of a sum or difference.
 7.8: Write as a single tangent function.
 7.9: Write as a single cosine function if is an angle in QII, i.e.
 7.10: \Write as a sum of two sinefunctions.
 7.11: Write as a product of two cosine functions.
 7.12: In the expression let What is the resulting expression?
 7.13: Solve the trigonometric equations exactly, if possible. Otherwise, ...
 7.14: Solve the trigonometric equations exactly, if possible. Otherwise, ...
 7.15: Solve the trigonometric equations exactly, if possible. Otherwise, ...
 7.16: Solve the trigonometric equations exactly, if possible. Otherwise, ...
 7.17: Determine whether is a conditional or an identity.
 7.18: Evaluate exactly.
 7.19: If 20. If cos x =0.26 and p 2 6 x 6 p,3p 2, find cosax
 7.20: find sin(2x).sin x =5 13 and p 6 x 6
 7.21: Express as a cotangent function.
 7.22: Calculate
 7.23: Determine an interval on which is onetoone,and determine the inve...
 7.24: Find the range of
 7.25: Solve for all real numbers.
 7.26: Solve for all real numbers.
 7.27: Solve for all real numbers.
 7.28: Show that the difference quotient for isPlot for a. b. c.What funct...
 7.29: Given tan and a. Find sin using the halfangle identity. b. Use the...
 7.1: Solve by completing the square:
 7.2: Write an equation of a line that passes through the point (2, 5) an...
 7.3: Write the equation of a circle with center (3, 1) and passing throu...
 7.4: Determine whether the relation is a function.
 7.5: Determine whether the function is odd or even.
 7.6: For the function , identify all of the transformations of .
 7.7: Find the composite function, and state the domain for and
 7.8: Find the inverse of the function
 7.9: Find the vertex of the parabola associated with the quadratic function
 7.10: Find a polynomial of minimum degree (there are many) that has the z...
 7.11: Use long division to nd the quotient and the remainder of
 7.12: Given the zero of the polynomial determine all the other zeros and ...
 7.13: Find the vertical and horizontal asymptotes of the function
 7.14: If $5,400 is invested at 2.25% compounded continuously, how much is...
 7.15: Use interval notation to express the domain of the function f(x) = ...
 7.16: Use properties of logarithms to simplify the expression
 7.17: Give an exact solution to the logarithmic equation .
 7.18: If money is invested in a saving account earning 4% compounded cont...
 7.19: Use a calculator to evaluate cos62. Round the answer to four decima...
 7.20: Angle of Inclination (Skiing). The angle of inclination of a mounta...
 7.21: Convert 105 to radians. Leave the answer in terms of .
 7.22: Find all of the exact values of , when and .
 7.23: Determine whether the equation is a conditional equation or an iden...
 7.24: Simplify and evaluate exactly.
 7.25: Evaluate exactly the expression .
 7.26: With a graphing calculator, plot Y1 sinxcos(3x), Y2 cos(4x), and Y3...
 7.27: Find the smallest positive value of x that makes the statement true...
Solutions for Chapter 7: Analytic Trigonometry
Full solutions for Algebra and Trigonometry  3rd Edition
ISBN: 9780470648032
Solutions for Chapter 7: Analytic Trigonometry
Get Full SolutionsChapter 7: Analytic Trigonometry includes 1023 full stepbystep solutions. Algebra and Trigonometry was written by and is associated to the ISBN: 9780470648032. Since 1023 problems in chapter 7: Analytic Trigonometry have been answered, more than 89317 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Algebra and Trigonometry, edition: 3.

Commuting matrices AB = BA.
If diagonalizable, they share n eigenvectors.

Dot product = Inner product x T y = XI Y 1 + ... + Xn Yn.
Complex dot product is x T Y . Perpendicular vectors have x T y = O. (AB)ij = (row i of A)T(column j of B).

Echelon matrix U.
The first nonzero entry (the pivot) in each row comes in a later column than the pivot in the previous row. All zero rows come last.

Ellipse (or ellipsoid) x T Ax = 1.
A must be positive definite; the axes of the ellipse are eigenvectors of A, with lengths 1/.JI. (For IIx II = 1 the vectors y = Ax lie on the ellipse IIA1 yll2 = Y T(AAT)1 Y = 1 displayed by eigshow; axis lengths ad

Four Fundamental Subspaces C (A), N (A), C (AT), N (AT).
Use AT for complex A.

Jordan form 1 = M 1 AM.
If A has s independent eigenvectors, its "generalized" eigenvector matrix M gives 1 = diag(lt, ... , 1s). The block his Akh +Nk where Nk has 1 's on diagonall. Each block has one eigenvalue Ak and one eigenvector.

Kirchhoff's Laws.
Current Law: net current (in minus out) is zero at each node. Voltage Law: Potential differences (voltage drops) add to zero around any closed loop.

lAII = l/lAI and IATI = IAI.
The big formula for det(A) has a sum of n! terms, the cofactor formula uses determinants of size n  1, volume of box = I det( A) I.

Left nullspace N (AT).
Nullspace of AT = "left nullspace" of A because y T A = OT.

Linearly dependent VI, ... , Vn.
A combination other than all Ci = 0 gives L Ci Vi = O.

Minimal polynomial of A.
The lowest degree polynomial with meA) = zero matrix. This is peA) = det(A  AI) if no eigenvalues are repeated; always meA) divides peA).

Norm
IIA II. The ".e 2 norm" of A is the maximum ratio II Ax II/l1x II = O"max· Then II Ax II < IIAllllxll and IIABII < IIAIIIIBII and IIA + BII < IIAII + IIBII. Frobenius norm IIAII} = L La~. The.e 1 and.e oo norms are largest column and row sums of laij I.

Nullspace N (A)
= All solutions to Ax = O. Dimension n  r = (# columns)  rank.

Orthogonal subspaces.
Every v in V is orthogonal to every w in W.

Partial pivoting.
In each column, choose the largest available pivot to control roundoff; all multipliers have leij I < 1. See condition number.

Pascal matrix
Ps = pascal(n) = the symmetric matrix with binomial entries (i1~;2). Ps = PL Pu all contain Pascal's triangle with det = 1 (see Pascal in the index).

Rank one matrix A = uvT f=. O.
Column and row spaces = lines cu and cv.

Spanning set.
Combinations of VI, ... ,Vm fill the space. The columns of A span C (A)!

Standard basis for Rn.
Columns of n by n identity matrix (written i ,j ,k in R3).

Vandermonde matrix V.
V c = b gives coefficients of p(x) = Co + ... + Cn_IXn 1 with P(Xi) = bi. Vij = (Xi)jI and det V = product of (Xk  Xi) for k > i.