Chapter 4.4, Problem 49E

To determine

The reference angle $\theta \text{'}$ and sketch $\theta$ and $\theta \text{'}$ in standardposition.

Answer to Problem 49E

The reference angle $\theta \text{'}$ is $\frac{\pi }{3}$

Explanation of Solution

Given info:

  $\theta =\frac{2\pi }{3}$

Formula used:

Let be $\theta$ an angle in standard position. Its reference angle $\theta \text{'}$ is the acute angleformed by the terminal side of $\theta$ and the horizontal axis.

Calculation:

Here we need to reference angle $\theta \text{'}$ when $\theta =\frac{2\pi }{3}$

We have

  $\begin{array}{l}\theta =\frac{2\pi }{3}\\ \theta \text{'}=\pi -\frac{2\pi }{3}=\frac{\pi }{3}\end{array}$

  

The reference angle $\theta \text{'}$ is $\frac{\pi }{3}$

Conclusion:

Thus,the reference angle $\theta \text{'}$ is $\frac{\pi }{3}$