Chapter 6, Problem 35SGA

To determine

To state: the amplitude and period for the function and also graph the function.

Answer to Problem 35SGA

The amplitude and period for the function is $\frac{1}{3}$ and $4\pi$ .

Explanation of Solution

Given information: The function is $y=-\frac{1}{3}\cos \frac{\theta }{2}$ .

Calculation:

The amplitude is depicted by the absolute value of the coefficient of the trigonometric function.

  $\begin{array}{l}\left|-\frac{1}{3}\right|=\frac{1}{3}\\ \frac{2\pi }{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}=4\pi \end{array}$

Period for the sine is depicted by $\frac{2\pi }{k}$ , where $k$ is the absolute value of the coefficient of $\theta$ .

The graph will be: