Chapter 6.4, Problem 21E

To determine

To state: the period of the function and then graph that function.

Answer to Problem 21E

  $8\pi$

Explanation of Solution

Given information:

  $y=\cos \frac{\theta }{4}$

Calculation:

The equation of sine function is as follows:

  $y=A\sin k\theta$..............(1)

Here $A$ is amplitude which is an absolute value of the coefficient and $k$ is the absolute value of coefficient $\theta$ .

Compare the given equation with equation (1) to get $k=\frac{1}{4}$ .

Now evaluate period of the function as follows:

  $\begin{array}{c}\text{Period}=\frac{2\pi }{k}\\ =\frac{2\pi }{\left(\frac{1}{4}\right)}\left[\text{Put the value of }k\right]\\ =2\pi \left(4\right)\\ =8\pi \end{array}$

Thus the period is $8\pi$ .

The graph of the function is as follows: