Chapter 12.6, Problem 40HP

To determine

To find: Draw the graph of a periodic function that has maximum value of $10$ and minimum value of $-10$ .

Answer to Problem 40HP

Period of the function $=1$

Explanation of Solution

Given information:

Periodic function

Maximum value $=10$

Minimum value $=-10$

Taking a function

  $y=10\sin \left(2\pi t\right)$

Graph of the above function is

  

On comparing above function with $y=a\sin bt$

We get

  $\begin{array}{l}a=10\\ b=2\pi \end{array}$

Therefore,

Amplitude $=\left|a\right|=10$

Period $=\frac{2\pi }{b}$

On substituting values

We get

  $\Rightarrow$ Period $=\frac{2\pi }{2\pi }$

  $\Rightarrow$ Period $=1$

Therefore,

Period of the function $=1$