Chapter 3.6, Problem 13E

To determine

To graph: The trigonometric and algebraic functions $y=\sin x,y={\sin }^{-1}x\text{ and }y=x$ on the same graphing window where $-\frac{\pi }{2}\le x\le \frac{\pi }{2}$ .

Explanation of Solution

Given information:

The trigonometric and algebraic functions $y=\sin x,y={\sin }^{-1}x\text{ and }y=x$ .

Graph:

Consider the provided trigonometric and algebraic functions $y=\sin x,y={\sin }^{-1}x\text{ and }y=x$ .

On a graphing window mark the points on coordinate axes. According to the question the value of x lies between $-\frac{\pi }{2}\le x\le \frac{\pi }{2}$ . The result obtained on screen is provided below,

The red curve denote the function $y=\sin x$ , blue curve denote the function $y={\sin }^{-1}x$ and the green line denote the function $y=x$ .

Interpretation:

The trigonometric and algebraic functions $y=\sin x,y={\sin }^{-1}x\text{ and }y=x$ when sketched on same graphing window where $-\frac{\pi }{2}\le x\le \frac{\pi }{2}$ it is observed that the graph of $y=\sin x$ is the reflection of the graph $y={\sin }^{-1}x$ about the line $y=x$ . Also the graph of $y={\sin }^{-1}x$ is the reflection of the graph $y=\sin x$ about the line $y=x$ .