 1.4.1: Define the six trigonometric functions in terms of the sides of a r...
 1.4.2: Explain how a point P1x, y2 on a circle of radius r determines an a...
 1.4.3: How is the radian measure of an angle determined?
 1.4.4: Explain what is meant by the period of a trigonometric function. Wh...
 1.4.5: What are the three Pythagorean identities for the trigonometric fun...
 1.4.6: How are the sine and cosine functions related to the other four tri...
 1.4.7: Where is the tangent function undefined?
 1.4.8: What is the domain of the secant function?
 1.4.9: Explain why the domain of the sine function must be restricted in o...
 1.4.10: Why do the values of cos1 x lie in the interval 30, p4?
 1.4.11: Is it true that tan 1tan1 x2 = x for all x? Is it true that tan1 ...
 1.4.12: Sketch the graphs of y = cos x and y = cos1 x on the same set of a...
 1.4.13: The function tan x is undefined at x = {p>2. How does this fact app...
 1.4.14: State the domain and range of sec1 x. .
 1.4.15: 1522. Evaluating trigonometric functions Evaluate the following exp...
 1.4.16: 1522. Evaluating trigonometric functions Evaluate the following exp...
 1.4.17: 1522. Evaluating trigonometric functions Evaluate the following exp...
 1.4.18: 1522. Evaluating trigonometric functions Evaluate the following exp...
 1.4.19: 1522. Evaluating trigonometric functions Evaluate the following exp...
 1.4.20: 1522. Evaluating trigonometric functions Evaluate the following exp...
 1.4.21: 1522. Evaluating trigonometric functions Evaluate the following exp...
 1.4.22: 1522. Evaluating trigonometric functions Evaluate the following exp...
 1.4.23: 2328. Evaluating trigonometric functions Evaluate the following exp...
 1.4.24: 2328. Evaluating trigonometric functions Evaluate the following exp...
 1.4.25: 2328. Evaluating trigonometric functions Evaluate the following exp...
 1.4.26: 2328. Evaluating trigonometric functions Evaluate the following exp...
 1.4.27: 2328. Evaluating trigonometric functions Evaluate the following exp...
 1.4.28: 2328. Evaluating trigonometric functions Evaluate the following exp...
 1.4.29: 2936. Trigonometric identities Prove that sec u = 1 cos u .
 1.4.30: 2936. Trigonometric identities Prove that tan u = sin u cos u .
 1.4.31: 2936. Trigonometric identities Prove that tan2 u + 1 = sec2 u.
 1.4.32: 2936. Trigonometric identities Prove that sin u csc u + cos u sec u...
 1.4.33: 2936. Trigonometric identities Prove that sec 1p>2  u2 = csc u.
 1.4.34: 2936. Trigonometric identities Prove that sec 1x + p2 = sec x.
 1.4.35: 2936. Trigonometric identities Find the exact value of cos 1p>122.
 1.4.36: 2936. Trigonometric identities Find the exact value of tan 13p>82.
 1.4.37: 3746. Solving trigonometric equations Solve the following equations...
 1.4.38: 3746. Solving trigonometric equations Solve the following equations...
 1.4.39: 3746. Solving trigonometric equations Solve the following equations...
 1.4.40: 3746. Solving trigonometric equations Solve the following equations...
 1.4.41: 3746. Solving trigonometric equations Solve the following equations...
 1.4.42: 3746. Solving trigonometric equations Solve the following equations...
 1.4.43: 3746. Solving trigonometric equations Solve the following equations...
 1.4.44: 3746. Solving trigonometric equations Solve the following equations...
 1.4.45: 3746. Solving trigonometric equations Solve the following equations...
 1.4.46: 3746. Solving trigonometric equations Solve the following equations...
 1.4.47: 4756. Inverse sines and cosines Without using a calculator, evaluat...
 1.4.48: 4756. Inverse sines and cosines Without using a calculator, evaluat...
 1.4.49: 4756. Inverse sines and cosines Without using a calculator, evaluat...
 1.4.50: 4756. Inverse sines and cosines Without using a calculator, evaluat...
 1.4.51: 4756. Inverse sines and cosines Without using a calculator, evaluat...
 1.4.52: 4756. Inverse sines and cosines Without using a calculator, evaluat...
 1.4.53: 4756. Inverse sines and cosines Without using a calculator, evaluat...
 1.4.54: 4756. Inverse sines and cosines Without using a calculator, evaluat...
 1.4.55: 4756. Inverse sines and cosines Without using a calculator, evaluat...
 1.4.56: 4756. Inverse sines and cosines Without using a calculator, evaluat...
 1.4.57: 5762. Righttriangle relationships Draw a right triangle to simplif...
 1.4.58: 5762. Righttriangle relationships Draw a right triangle to simplif...
 1.4.59: 5762. Righttriangle relationships Draw a right triangle to simplif...
 1.4.60: 5762. Righttriangle relationships Draw a right triangle to simplif...
 1.4.61: 5762. Righttriangle relationships Draw a right triangle to simplif...
 1.4.62: 5762. Righttriangle relationships Draw a right triangle to simplif...
 1.4.63: 6364. Identities Prove the following identities. cos1 x + cos1 1...
 1.4.64: 6364. Identities Prove the following identities. sin1 y + sin1 1...
 1.4.65: 6566. Verifying identities Sketch a graph of the given pair of func...
 1.4.66: 6566. Verifying identities Sketch a graph of the given pair of func...
 1.4.67: 6774. Evaluating inverse trigonometric functions Without using a ca...
 1.4.68: 6774. Evaluating inverse trigonometric functions Without using a ca...
 1.4.69: 6774. Evaluating inverse trigonometric functions Without using a ca...
 1.4.70: 6774. Evaluating inverse trigonometric functions Without using a ca...
 1.4.71: 6774. Evaluating inverse trigonometric functions Without using a ca...
 1.4.72: 6774. Evaluating inverse trigonometric functions Without using a ca...
 1.4.73: 6774. Evaluating inverse trigonometric functions Without using a ca...
 1.4.74: 6774. Evaluating inverse trigonometric functions Without using a ca...
 1.4.75: 7580. Righttriangle relationships Use a right triangle to simplify...
 1.4.76: 7580. Righttriangle relationships Use a right triangle to simplify...
 1.4.77: 7580. Righttriangle relationships Use a right triangle to simplify...
 1.4.78: 7580. Righttriangle relationships Use a right triangle to simplify...
 1.4.79: 7580. Righttriangle relationships Use a right triangle to simplify...
 1.4.80: 7580. Righttriangle relationships Use a right triangle to simplify...
 1.4.81: 8182. Righttriangle pictures Express u in terms of x using the inv...
 1.4.82: 8182. Righttriangle pictures Express u in terms of x using the inv...
 1.4.83: Explain why or why not Determine whether the following statements a...
 1.4.84: 8487. One function gives all six Given the following information ab...
 1.4.85: 8487. One function gives all six Given the following information ab...
 1.4.86: 8487. One function gives all six Given the following information ab...
 1.4.87: 8487. One function gives all six Given the following information ab...
 1.4.88: 8891. Amplitude and period Identify the amplitude and period of the...
 1.4.89: 8891. Amplitude and period Identify the amplitude and period of the...
 1.4.90: 8891. Amplitude and period Identify the amplitude and period of the...
 1.4.91: 8891. Amplitude and period Identify the amplitude and period of the...
 1.4.92: 9295. Graphing sine and cosine functions Beginning with the graphs ...
 1.4.93: 9295. Graphing sine and cosine functions Beginning with the graphs ...
 1.4.94: 9295. Graphing sine and cosine functions Beginning with the graphs ...
 1.4.95: 9295. Graphing sine and cosine functions Beginning with the graphs ...
 1.4.96: 9697. Designer functions Design a sine function with the given prop...
 1.4.97: 9697. Designer functions Design a sine function with the given prop...
 1.4.98: Field goal attempt Near the end of the 1950 Rose Bowl football game...
 1.4.99: A surprising result The Earth is approximately circular in cross se...
 1.4.100: Daylight function for 40_ N Verify that the function has the follow...
 1.4.101: Block on a spring A light block hangs at rest from the end of a spr...
 1.4.102: Approaching a lighthouse A boat approaches a 50fthigh lighthouse ...
 1.4.103: Ladders Two ladders of length a lean against opposite walls of an a...
 1.4.104: Pole in a corner A pole of length L is carried horizontally around ...
 1.4.105: Littleknown fact The shortest day of the year occurs on the winter...
 1.4.106: Viewing angles An auditorium with a flat floor has a large flatpane...
 1.4.107: Area of a circular sector Prove that the area of a sector of a circ...
 1.4.108: Law of cosines Use the figure to prove the law of cosines (which is...
 1.4.109: Law of sines Use the figure to prove the law of sines: sin A a = si...
Solutions for Chapter 1.4: Calculus: Early Transcendentals 2nd Edition
Full solutions for Calculus: Early Transcendentals  2nd Edition
ISBN: 9780321947345
Solutions for Chapter 1.4
Get Full SolutionsCalculus: Early Transcendentals was written by and is associated to the ISBN: 9780321947345. Chapter 1.4 includes 109 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. Since 109 problems in chapter 1.4 have been answered, more than 56693 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 2.

Circular functions
Trigonometric functions when applied to real numbers are circular functions

Complex fraction
See Compound fraction.

Component form of a vector
If a vector’s representative in standard position has a terminal point (a,b) (or (a, b, c)) , then (a,b) (or (a, b, c)) is the component form of the vector, and a and b are the horizontal and vertical components of the vector (or a, b, and c are the x, y, and zcomponents of the vector, respectively)

Compounded monthly
See Compounded k times per year.

Differentiable at x = a
ƒ'(a) exists

Divisor of a polynomial
See Division algorithm for polynomials.

Inverse properties
a + 1a2 = 0, a # 1a

Multiplication principle of counting
A principle used to find the number of ways an event can occur.

Multiplicative inverse of a complex number
The reciprocal of a + bi, or 1 a + bi = a a2 + b2 ba2 + b2 i

Nautical mile
Length of 1 minute of arc along the Earth’s equator.

Piecewisedefined function
A function whose domain is divided into several parts with a different function rule applied to each part, p. 104.

Pointslope form (of a line)
y  y1 = m1x  x 12.

Polynomial in x
An expression that can be written in the form an x n + an1x n1 + Á + a1x + a0, where n is a nonnegative integer, the coefficients are real numbers, and an ? 0. The degree of the polynomial is n, the leading coefficient is an, the leading term is anxn, and the constant term is a0. (The number 0 is the zero polynomial)

Projection of u onto v
The vector projv u = au # vƒvƒb2v

Quadratic formula
The formula x = b 2b2  4ac2a used to solve ax 2 + bx + c = 0.

Quadric surface
The graph in three dimensions of a seconddegree equation in three variables.

Range (in statistics)
The difference between the greatest and least values in a data set.

Reexpression of data
A transformation of a data set.

Tangent line of ƒ at x = a
The line through (a, ƒ(a)) with slope ƒ'(a) provided ƒ'(a) exists.

yaxis
Usually the vertical coordinate line in a Cartesian coordinate system with positive direction up, pp. 12, 629.