 7.1.1: In Exercises 1 8, evaluate each expression (as in Example 1).
 7.1.2: In Exercises 1 8, evaluate each expression (as in Example 1).
 7.1.3: In Exercises 1 8, evaluate each expression (as in Example 1).
 7.1.4: In Exercises 1 8, evaluate each expression (as in Example 1).
 7.1.5: In Exercises 1 8, evaluate each expression (as in Example 1).
 7.1.6: In Exercises 1 8, evaluate each expression (as in Example 1).
 7.1.7: In Exercises 1 8, evaluate each expression (as in Example 1).
 7.1.8: In Exercises 1 8, evaluate each expression (as in Example 1).
 7.1.9: (a) List four positive realnumber values of t for which cos t 0. (...
 7.1.10: (a) List four positive real numbers t such that sin t 1/2. (b) List...
 7.1.11: In Exercises 1114, use a calculator to evaluate the six trigonometr...
 7.1.12: In Exercises 1114, use a calculator to evaluate the six trigonometr...
 7.1.13: In Exercises 1114, use a calculator to evaluate the six trigonometr...
 7.1.14: In Exercises 1114, use a calculator to evaluate the six trigonometr...
 7.1.15: In Exercises 1522, check that both sides of the identity are indeed...
 7.1.16: In Exercises 1522, check that both sides of the identity are indeed...
 7.1.17: In Exercises 1522, check that both sides of the identity are indeed...
 7.1.18: In Exercises 1522, check that both sides of the identity are indeed...
 7.1.19: In Exercises 1522, check that both sides of the identity are indeed...
 7.1.20: In Exercises 1522, check that both sides of the identity are indeed...
 7.1.21: In Exercises 1522, check that both sides of the identity are indeed...
 7.1.22: In Exercises 1522, check that both sides of the identity are indeed...
 7.1.23: In Exercises 23 and 24, show that the equation is not an identity b...
 7.1.24: In Exercises 23 and 24, show that the equation is not an identity b...
 7.1.25: If sin t 3/5 and , compute cos t and tan t.
 7.1.26: If cos t 5/13 and , compute sin t and cot t.
 7.1.27: If and , compute tan t.
 7.1.28: If and sin s 0, compute tan s.
 7.1.29: If tan a 12/5 and cos a 0, compute sec a, cos a, and sin a.
 7.1.30: If and cos u 0, compute csc u and sin u.
 7.1.31: In the expression , make the substitution , and show that the resul...
 7.1.32: Make the substitution u 2 cos u in the expression , and simplify th...
 7.1.33: In the expression 1/(u2 25)3/2, make the substitution , and show th...
 7.1.34: In the expression 1/(x2 5)2 , replace x by and show that the result...
 7.1.35: In the expression let where , and simplify the result.
 7.1.36: In the expression , let , and simplify the result.
 7.1.37: (a) If sin t 2/3, find sin(t). (b) If sin f 1/4, find sin(f). (c) I...
 7.1.38: (a) If sin t 0.35, find sin(t). (b) If sin f 0.47, find sin(f). (c)...
 7.1.39: If cos t 1/3 , compute the following: (a) sin(t) cos(t) (b) sin2 (t...
 7.1.40: If , compute: (a) sin s (c) cos s (b) cos(s) (d) tan s tan(s)
 7.1.41: In Exercises 41 and 42, use one of the identities cos(t 2pk) cos t ...
 7.1.42: In Exercises 41 and 42, use one of the identities cos(t 2pk) cos t ...
 7.1.43: In Exercises 43 46, use the Pythagorean identities to simplify the ...
 7.1.44: In Exercises 43 46, use the Pythagorean identities to simplify the ...
 7.1.45: In Exercises 43 46, use the Pythagorean identities to simplify the ...
 7.1.46: In Exercises 43 46, use the Pythagorean identities to simplify the ...
 7.1.47: In Exercises 4754, prove that the equations are identities.
 7.1.48: In Exercises 4754, prove that the equations are identities.
 7.1.49: In Exercises 4754, prove that the equations are identities.
 7.1.50: In Exercises 4754, prove that the equations are identities.
 7.1.51: In Exercises 4754, prove that the equations are identities.
 7.1.52: In Exercises 4754, prove that the equations are identities.
 7.1.53: In Exercises 4754, prove that the equations are identities.
 7.1.54: In Exercises 4754, prove that the equations are identities.
 7.1.55: If , evaluate
 7.1.56: If sec t (b2 1)/2b and , find tan t and sin t. (Note: b is negative...
 7.1.57: Use the accompanying figure to explain why the following four ident...
 7.1.58: Use two of the results in Exercise 57 to verify the identity tan(t ...
 7.1.59: In the equation x4 6x2 y2 y4 32, make the substitutions and and sho...
 7.1.60: Suppose that tan u 2 and 0 u p/2. (a) Compute sin u and cos u. (b) ...
 7.1.61: In this exercise, we are going to find the minimum value of the fun...
 7.1.62: Let . (a) Set your calculator in the radian mode and complete the t...
 7.1.63: Consider the equation 2 sin2 t sin t 2 sin t cos t cos t (a) Evalua...
 7.1.64: Suppose that f(t) (sin t cos t)(2 sin t 1)(2 cos t 1)(tan t 1) (a) ...
 7.1.65: In Section 6.1 we pointed out that one of the advantages in using r...
 7.1.66: In Section 6.1 we pointed out that one of the advantages in using r...
 7.1.67: In Section 6.1 we pointed out that one of the advantages in using r...
 7.1.68: In Section 6.1 we pointed out that one of the advantages in using r...
 7.1.69: The figure on the following page shows two xy coordinate systems. ...
Solutions for Chapter 7.1: TRIGONOMETRIC FUNCTIONS OF REAL NUMBERS
Full solutions for Precalculus: With Unit Circle Trigonometry (with Interactive Video Skillbuilder CDROM) (Available 2010 Titles Enhanced Web Assign)  4th Edition
ISBN: 9780534402303
Solutions for Chapter 7.1: TRIGONOMETRIC FUNCTIONS OF REAL NUMBERS
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Precalculus: With Unit Circle Trigonometry (with Interactive Video Skillbuilder CDROM) (Available 2010 Titles Enhanced Web Assign) was written by and is associated to the ISBN: 9780534402303. This textbook survival guide was created for the textbook: Precalculus: With Unit Circle Trigonometry (with Interactive Video Skillbuilder CDROM) (Available 2010 Titles Enhanced Web Assign), edition: 4. Since 69 problems in chapter 7.1: TRIGONOMETRIC FUNCTIONS OF REAL NUMBERS have been answered, more than 25426 students have viewed full stepbystep solutions from this chapter. Chapter 7.1: TRIGONOMETRIC FUNCTIONS OF REAL NUMBERS includes 69 full stepbystep solutions.

Anchor
See Mathematical induction.

Blind experiment
An experiment in which subjects do not know if they have been given an active treatment or a placebo

Definite integral
The definite integral of the function ƒ over [a,b] is Lbaƒ(x) dx = limn: q ani=1 ƒ(xi) ¢x provided the limit of the Riemann sums exists

Determinant
A number that is associated with a square matrix

Discriminant
For the equation ax 2 + bx + c, the expression b2  4ac; for the equation Ax2 + Bxy + Cy2 + Dx + Ey + F = 0, the expression B2  4AC

Elements of a matrix
See Matrix element.

Equation
A statement of equality between two expressions.

Focus, foci
See Ellipse, Hyperbola, Parabola.

Identity function
The function ƒ(x) = x.

Independent variable
Variable representing the domain value of a function (usually x).

Limit
limx:aƒ1x2 = L means that ƒ(x) gets arbitrarily close to L as x gets arbitrarily close (but not equal) to a

Linear equation in x
An equation that can be written in the form ax + b = 0, where a and b are real numbers and a Z 0

Logarithmic reexpression of data
Transformation of a data set involving the natural logarithm: exponential regression, natural logarithmic regression, power regression

LRAM
A Riemann sum approximation of the area under a curve ƒ(x) from x = a to x = b using x1 as the lefthand endpoint of each subinterval

Open interval
An interval that does not include its endpoints.

Opens upward or downward
A parabola y = ax 2 + bx + c opens upward if a > 0 and opens downward if a < 0.

Ordered set
A set is ordered if it is possible to compare any two elements and say that one element is “less than” or “greater than” the other.

Positive numbers
Real numbers shown to the right of the origin on a number line.

Slope
Ratio change in y/change in x

Work
The product of a force applied to an object over a given distance W = ƒFƒ ƒAB!ƒ.