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 ${55}^0$

Explanation of Solution

Given info:

  $\theta =-{125}^0$

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 $\theta =-{125}^0$

We have

  $\begin{array}{l}\theta =-{125}^0\\ \theta =360-125={235}^0\text{ (Co terminal angle)}\\ \theta \text{'}=235-180={55}^0\end{array}$

  

The reference angle $\theta \text{'}$ is ${55}^0$

Conclusion:

Thus,the reference angle $\theta \text{'}$ is ${55}^0$