Chapter 3, Problem 76RE

a.

To determine

To find: The relationship between these two function that involves the derivative.

Answer to Problem 76RE

At some points derivative does not exist where the graph of $\frac{\left|\sin x\right|}{\sin x}$ break where $\sin x=0\mathrm{that}isx=0,\pm \pi ,\pm 2\pi$

  

Explanation of Solution

Given information: $y_1={\cos }^{-1}(\cos (x))\mathrm{and}{y}_2=\frac{\left|\sin x\right|}{\sin x}$ .

Calculation: $y_1={\cos }^{-1}(\cos (x))\mathrm{and}{y}_2=\frac{\left|\sin x\right|}{\sin x}$ .

Firstly draw the graph of $y_1={\cos }^{-1}(\cos (x))\mathrm{and}{y}_2=\frac{\left|\sin x\right|}{\sin x}$

Red is $y_1={\cos }^{-1}(\cos (x))$ and blue is $y_2=\frac{\left|\sin x\right|}{\sin x}$

  

At some points derivative does not exist where the graph of $\frac{\left|\sin x\right|}{\sin x}$ break where $\sin x=0\mathrm{that}isx=0,\pm \pi ,\pm 2\pi$ .

b.

To determine

To find :The function $y_2$ that relates the function $y_1={\sin }^{-1}(\sin (x))$ in the same way.

Answer to Problem 76RE

  $y_2=\frac{\left|\cos x\right|}{\cos x}$ is derivative of $y_1={\sin }^{-1}(\sin (x))$ .

Explanation of Solution

Given:

  $y_1={\sin }^{-1}(\sin (x))$ .

Calculation: $y_1={\sin }^{-1}(\sin (x))$

  $y_2=\frac{\left|\cos x\right|}{\cos x}$ is derivative of $y_1={\sin }^{-1}(\sin (x))$ .