Chapter 12.7, Problem 5GP

To determine

To determine the period of the given function and graph it.

Answer to Problem 5GP

Period $=\pi$

Explanation of Solution

Given:

  $y=\csc 2\theta$

Concept used:

Amplitude is the distance between the center line of the function and the top or bottom of the function.

Period is the distance between two peaks of the graph.

The generalized equation for a cosine function is:

  $y=A\csc \left(Bx\right)$

Amplitude $=A$

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

Calculation:

For $y=\csc 2\theta$ ,

Comparing with the general cosine equation $y=A\csc \left(Bx\right)$ ,

  $B=2$

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

  $\begin{array}{l}=\frac{2\pi }{2}\\ =\pi \end{array}$

The period of the given function is $\pi$ .

Graph:

The graph of $y=\csc 2\theta$ :

  

Conclusion:

Therefore, the period of the given function is $\pi$ .