   Chapter 1.5, Problem 76E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# (a) Graph the function f(x) = sin(sin‒1 x) and explain the appearance of the graph.(b) Graph the function g(x) = sin‒1(sin x). How do you explain the appearance of this graph?

(a)

To determine

To Explain: The graph of the function. f(x)=sin(sin1x) .

Explanation

Use online graph calculator and draw the graph of f(x)=sin(sin1x) as shown below in Figure1.

Notice that, Figure 1is the graph of y = x on the domain [−1,1].

As sin x and sin1x are the inverse functions, sin(sin1x)=x .

Thus, the given function reduces to, y = x.

It is known the fact that the domain of sine function is for all real numbers and the range of  the sine function is [π2,π2] .

Also, the fact that the domain of inverse of sine function is [-1,1] and the range of the inverse of the function is [π2,π2]

(b)

To determine

To explain: The appearance of the graph of. g(x)=sin1(sinx) .

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