Question

Graph the given functions on the same screen. How are these graphs related?

79. \(y = \sin x,\,\,\, - \frac{\pi }{2} \le x \le \frac{\pi }{2};\,\,\,\,y = {\sin ^{ - 1}}x;\,\,\,\,y = x\)

Short answer

The graph is shown below:

The graph of \({\sin ^{ - 1}}x\) is the reflection of the graph of \(\sin x\) around the line \(y = x\).

Step-by-step solution

Graph of the given function on the same screen

The procedure to draw the graph of the given equation by using the graphing calculator is as follows:

To check the answer visually draw the graph of the given functionby using the graphing calculator as shown below:

1. Open the graphing calculator. Enter the equation\(\sin X\)in the\({Y_1}\)tab.
2. Set the window\( - \frac{\pi }{2} \le x \le \frac{\pi }{2}\).
3. Enter the equation\({\sin ^{ - 1}}X\)in the\({Y_2}\)tab.
4. Enter the equation\(X\)in the\({Y_3}\)tab.
5. Enter the “GRAPH” button in the graphing calculator.

Visualization of the graph of the functions is shown below:

Determine the relation of graphs

The graph of \({f^{ - 1}}\) is determined by reflectingthe graph of \(f\) about the line \(y = x\).

Thus, the graph of \({\sin ^{ - 1}}x\) is the reflection of the graph of \(\sin x\) around the line \(y = x\).