1 Functions 2 Limits 3 Derivatives 4 Applications Of The Derivatives 5 Integration 6 Applications Of Integration 7 Integration Techniques 8 Sequences And Infinite Series 9 Power Series 10 Parametric And Polar Curves 11 Vectors And Vector-valued Functions 12 Functions Of Several Variables 13 Multiple Integration 14 Vector Calculus D1 Differential Equations D2 Second-order Differential Equations A Algebra Review expand_more
1.1 Review Of Functions 1.2 Representing Functions 1.3 Inverse, Exponential, And Logarithmic Functions 1.4 Trigonometric Functions And Their Inverses Chapter Questions expand_more
Problem 1E: Define the six trigonometric functions in terms of the sides of a right triangle. Problem 2E Problem 3E: How is the radian measure of an angle determined? Problem 4E: Explain what is meant by the period of a trigonometric function. What are the periods of the six... Problem 5E: What are the three Pythagorean identities for the trigonometric functions? Problem 6E: How are the sine and cosine functions related to the other four trigonometric functions? Problem 7E: Where is the tangent function undefined? Problem 8E: What is the domain of the secant function? Problem 9E: Explain why the domain of the sine function must be restricted in order to define its inverse... Problem 10E: Why do the values of cos1 x lie in the interval [0, ]? Problem 11E Problem 12E Problem 13E: The function tan x is undefined at x = /2. How does this fact appear in the graph of y = tan1 x? Problem 14E: State the domain and range of sec1 x. Problem 15E Problem 16E: Evaluating trigonometric functions Evaluate the following expressions using a unit circle. Use a... Problem 17E Problem 18E Problem 19E Problem 20E Problem 21E Problem 22E: Evaluating trigonometric functions Evaluate the following expressions using a unit circle. Use a... Problem 23E Problem 24E Problem 25E Problem 26E Problem 27E Problem 28E: Evaluating trigonometric functions Evaluate the following expressions or state that the quantity is... Problem 29E: Trigonometric identities 29. Prove that sec=1cos. Problem 30E: Trigonometric identities 30. Prove that tan=sincos. Problem 31E: Trigonometric identities 31. Prove that tan2 + 1 = sec2 . Problem 32E: Trigonometric identities 32. Prove that sincsc+cossec=1. Problem 33E: Trigonometric identities 33. Prove that sec (/2 ) = csc . Problem 34E: Trigonometric identities 34. Prove that sec (x + ) = sec x. Problem 35E Problem 36E Problem 37E: Solving trigonometric equations Solve the following equations. 37. tan x = 1 Problem 38E: Solving trigonometric equations Solve the following equations. 38. 2 cos + = 0 Problem 39E: Solving trigonometric equations Solve the following equations. 39. sin2=14,02 Problem 40E: Solving trigonometric equations Solve the following equations. 40. cos2=12,02 Problem 41E: Solving trigonometric equations Solve the following equations. 41. 2sinx1=0 Problem 42E: Solving trigonometric equations Solve the following equations. 42. sin3x=22,0x2 Problem 43E: Solving trigonometric equations Solve the following equations. 43. cos 3x = sin 3x, 0 x 2 Problem 44E: Solving trigonometric equations Solve the following equations. 44. sin2 1 = 0 Problem 45E: Solving trigonometric equations Solve the following equations. 44. sin cos = 0, 0 2 Problem 46E: Solving trigonometric equations Solve the following equations. 46. tan2 2 = 1, 0 Problem 47E: Inverse sines and cosines Without using a calculator, evaluate the following expressions or state... Problem 48E: Inverse sines and cosines Without using a calculator, evaluate the following expressions or state... Problem 49E: Inverse sines and cosines Without using a calculator, evaluate the following expressions or state... Problem 50E: Inverse sines and cosines Without using a calculator, evaluate the following expressions or state... Problem 51E: Inverse sines and cosines Without using a calculator, evaluate the following expressions or state... Problem 52E: Inverse sines and cosines Without using a calculator, evaluate the following expressions or state... Problem 53E: Inverse sines and cosines Without using a calculator, evaluate the following expressions or state... Problem 54E: Inverse sines and cosines Without using a calculator, evaluate the following expressions or state... Problem 55E: Inverse sines and cosines Without using a calculator, evaluate the following expressions or state... Problem 56E: Inverse sines and cosines Without using a calculator, evaluate the following expressions or state... Problem 57E: Right-triangle relationships Draw a right triangle to simplify the given expressions. Assume x 0.... Problem 58E: Right-triangle relationships Draw a right triangle to simplify the given expressions. Assume x 0.... Problem 59E: Right-triangle relationships Draw a right triangle to simplify the given expressions. Assume x 0.... Problem 60E: Right-triangle relationships Draw a right triangle to simplify the given expressions. Assume x 0.... Problem 61E: Right-triangle relationships Draw a right triangle to simplify the given expressions. Assume x 0.... Problem 62E: Right-triangle relationships Draw a right triangle to simplify the given expressions. Assume x 0.... Problem 63E: Identities Prove the following identities. 63. cos1 x + cos1 (x) = Problem 64E Problem 65E Problem 66E Problem 67E: Evaluating inverse trigonometric functions Without using a calculator, evaluate or simplify the... Problem 68E Problem 69E: Evaluating inverse trigonometric functions Without using a calculator, evaluate or simplify the... Problem 70E Problem 71E Problem 72E: Evaluating inverse trigonometric functions Without using a calculator, evaluate or simplify the... Problem 73E: Evaluating inverse trigonometric functions Without using a calculator, evaluate or simplify the... Problem 74E Problem 75E: Right-triangle relationships Use a right triangle to simplify the given expressions. Assume x 0.... Problem 76E: Right-triangle relationships Use a right triangle to simplify the given expressions. Assume x 0.... Problem 77E: Right-triangle relationships Use a right triangle to simplify the given expressions. Assume x 0.... Problem 78E: Right-triangle relationships Use a right triangle to simplify the given expressions. Assume x 0.... Problem 79E: Right-triangle relationships Use a right triangle to simplify the given expressions. Assume x 0.... Problem 80E Problem 81E: Right-triangle pictures Express in terms of x using the inverse sine, inverse tangent, and inverse... Problem 82E: Right-triangle pictures Express in terms of x using the inverse sine, inverse tangent, and inverse... Problem 83E: Explain why or why not Determine whether the following statements are true and give an explanation... Problem 84E: One function gives all six Given the following information about one trigonometric function,... Problem 85E: One function gives all six Given the following information about one trigonometric function,... Problem 86E: One function gives all six Given the following information about one trigonometric function,... Problem 87E: One function gives all six Given the following information about one trigonometric function,... Problem 88E Problem 89E: Amplitude and period Identify the amplitude and period of the following functions. 89. g() = 3 cos... Problem 90E Problem 91E: Amplitude and period Identify the amplitude and period of the following functions. 91. q(x) = 3.6... Problem 92E: Graphing sine and cosine functions Beginning with the graphs of y = sin x or y = cos x, use shifting... Problem 93E: Graphing sine and cosine functions Beginning with the graphs of y = sin x or y = cos x, use shifting... Problem 94E: Graphing sine and cosine functions Beginning with the graphs of y = sin x or y = cos x, use shifting... Problem 95E: Graphing sine and cosine functions Beginning with the graphs of y = sin x or y = cos x, use shifting... Problem 96E Problem 97E: Designer functions Design a sine function with the given properties. 97. It has a period of 24 hr... Problem 98E: Field goal attempt Near the end of the 1950 Rose Bowl football game between the University of... Problem 99E: A surprising result The Earth is approximately circular in cross section, with a circumference at... Problem 100E: Daylight function for 40 N Verify that the function D(t)=2.8sin(2365(t81))+12 has the following... Problem 101E: Block on a spring A light block hangs at rest from the end of a spring when it is pulled down 10 cm... Problem 102E Problem 103E: Ladders Two ladders of length a lean against opposite walls of an alley with their feet touching... Problem 104E: Pole in a corner A pole of length L is carried horizontally around a corner where a 3-ft-wide... Problem 105E: Little-known fact The shortest day of the year occurs on the winter solstice (near December 21) and... Problem 106E: Viewing angles An auditorium with a flat floor has a large flat-panel television on one wall. The... Problem 107E: Area of a circular sector Prove that the area of a sector of a circle of radius r associated with a... Problem 108E: Law of cosines Use the figure to prove the law of cosines (which is a generalization of the... Problem 109E: Law of sines Use the figure to prove the law of sines: sinAa=sinBb=sinCc. format_list_bulleted