Chapter 12.6, Problem 39HP

To determine

To determine whether the period of sine curve is a multiple of $\pi$ or not.

Answer to Problem 39HP

The period of sine curve is sometimes multiple of $\pi$ .

Explanation of Solution

Given:

Sine curve

Concept used:

Period is the length of one cycle.

Calculation:

First consider the function

  $f\left(x\right)=\sin x$

Period $=\frac{2\pi }{b}=\frac{2\pi }{1}=2\pi$

This is a multiple of $\pi$ .

Now consider the function,

  $g\left(x\right)=\sin 4x$

Period $=\frac{2\pi }{b}=\frac{2\pi }{4}=\frac{\pi }{2}$ .

This is not a multiple of $\pi$ .

Conclusion:

Therefore, the period of sine curve is sometimes multiple of $\pi$ .