Chapter 4.4, Problem 59E

To determine

To find:The reference angle ${\theta }^{\text{'}}$ and sketch $\theta$ in standard position if $\theta =208°$ .

Answer to Problem 59E

The reference angle ${\theta }^{\text{'}}$ is $28°$ .

Explanation of Solution

Given information:

The given angle $\theta =208°$ .

Calculation:

A reference angle ${\theta }^{\text{'}}$ is defined as the acute angle made by the terminal side of the angle $\theta$ and the horizontal axis.

Since, the value of $\theta$ is $208°$ and it lies in quadrant III. Sketch the standard position of angle $\theta$ .

  

Calculate the reference angle.

  $\begin{array}{c}{\theta }^{\text{'}}=208°-180°\\ =28°\end{array}$

Therefore, the reference angle ${\theta }^{\text{'}}$ is $28°$ .