Calculus of a Single Variable
11th Edition
ISBN: 9781337275361
Author: Ron Larson, Bruce H. Edwards
Publisher: Cengage Learning
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Chapter P.4, Problem 70E
To determine
How to restrict the domain of the sine function so that it becomes a one to one function.
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- Graphical Reasoning Use the formulas for the area of a circular sector and arc length given in Section 1.1. (a) For =0.8, write the area and arc length as functions of r. What is the domain of each function? Use a graphing utility to graph the functions. Use the graphs to determine which function changes more rapidly as r increases. Explain. (b) For r=10 centimeters, write the area and arc length as functions of . What is the domain of each function? Use the graphing utility to graph the functions.arrow_forwardUsing the Unit Circle Use the unit circle to verify that the cosine and secant functions are even and that the sine, cosecant, tangent, and cotangent functions are odd.arrow_forwardThink About It Complete the table. (a) Discuss the behavior of the sine function for 090. (b) Discuss the behavior of the cosine function for 090. (c) Use the definitions of the sine and cosine functions to explain the results of parts a and b.arrow_forward
- HOW DO YOU SEE IT? Use the figure below. (a) Are all of the trigonometric functions of t defined? Explain. (b) For those trigonometric functions that are defined, determine whether the sign of the trigonometric function is positive or negative. Explain.arrow_forwardHyperbolic sine Function The hyperbolic sine function is defined by sinh(x)=exex2 a Sketch the graph of this function using graphical addition as in Exercise 17. b Use the definition to show that sinh(x)=sinh(x) Hyperbolic Cosine Function The hyperbolic cosine function is defined by cosh(x)=ex+ex2 a Sketch the graphs of the functions y=13ex and y=12ex on the same axes, and use graphical addition see Section 2.7 to sketch the graph of y=cosh(x). b Use the definition to show that cosh(x)=cosh(x).arrow_forwardHeight of the Space Shuttle An observer views the space shuttle from a distance of 2 mi from the launch pad. a Express the height of the space shuttle as a function of the angle of elevation . b Express the angle of elevation as a function of the height h of the space shuttle.arrow_forward
- SKILLS Evaluating Expression Involving Trignometric Functions Evaluate each expression under the given conditions. sin(); tan=43, is in Quadrant III, sin=1010, is in Quadrant IV.arrow_forwardCONCEPTS a To define the inverse sine function, we restrict the domain of sine to the interval ______. On this interval the sine function is one-to-one, and its inverse function sin1 is defined by sin1x=ysin=______. For example, sin112= because sin ______ = _______. b To define the inverse cosine function, we restrict the domain of cosine to the interval __________. On this interval the cosine function is one-to-one, and its inverse function cos1 is defined by cos1x=ycos=. For example, cos112= because cos _______ = ________.arrow_forwardHeight of a Pole A 50-ft pole casts a shadow as shown in the figure. a Express the angle of elevation of the sun as a function of the length s of the shadow . b Find the angle of elevation of the sun when the shadow is 20 ft long.arrow_forward
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