Chapter SH, Problem 12.19EP

To determine

To find: The amplitude, period of given function. And then graph the function.

Answer to Problem 12.19EP

The amplitude of the given function is $\frac{1}{2}$ and the period is $\frac{2\pi }{3}$ and the graph is shown below.

Explanation of Solution

Given:

The given function is:

  $y=\frac{1}{2}\sin 3\theta$ .

Consider the sine function:

  $y=A\sin \left(B\left(x-C\right)\right)+D$

The amplitude and period of the sine function is given as:

The amplitude is $\left|A\right|$ .

The period is $\frac{2\pi }{B}$ .

By comparing the given function by the above function the amplitude and period are as given:

The amplitude of the given function is $\frac{1}{2}$ .

The period is $\frac{2\pi }{3}$ .

The graph of the given function is as:

  

Therefore the amplitude of the given function is $\frac{1}{2}$ and the period is $\frac{2\pi }{3}$ and the graph is shown above.