Chapter 4.4, Problem 21E

To determine

To find: The reference angle.

Answer to Problem 21E

The reference angle is $55°$

Explanation of Solution

Given information:

The value of angle

  $\theta \prime =360°-\theta$

Calculation:

Calculate the angle in standard position .The reference angle is the acute angle $\theta$ formed by the terminal side of $\theta$ and the horizontal axis.

Calculate the $\sin \theta >0$ and $\cos \theta <0$ .

Now consider that,

  $\theta =11.6°$ radian

Therefore,

  $\begin{array}{c}\pi \text{ radian}=180°\\ 1\text{ radian}=\frac{180}{\pi }\\ \theta =11.6\left(\frac{180}{\pi }\right)\\ =305°\end{array}$

The angle lies in the 4^th quadrant .The reference angle for any angle in the 4^th quadrant given by,

  $\theta \prime =360°-\theta$

Calculate the reference angle.

  $\begin{array}{l}\theta \prime =360°-\theta \\ \theta \prime =360°-305°\\ \theta \prime =55°\end{array}$

Therefore, the reference angle is $\theta \prime =55°$ .