Chapter 13.1, Problem 55WE

To determine

To Find: The measure of the angle between $0$ and $2\pi$ that is conterminal with $\alpha$ .

Answer to Problem 55WE

The measure of the angle between $0$ and $2\pi$ that is conterminal with $\alpha$ is about $1.84$ radians.

Explanation of Solution

Given information:

Given measure is $\alpha =8.12$ .

Calculation:

In order to convert the given measure to degrees, multiply by $\frac{{180}^{°}}{\pi }$ .

  $8.12$ radians,

  $\begin{array}{l}=\mathrm{8.12.}\frac{{180}^{°}}{\pi }\\ ={465.24}^{°}\end{array}$

Find the measure of the angle that is conterminal with $\alpha$ .

Since ${465.24}^{°}$ lies in the second quadrant, the conterminal will be ${465.24}^{°}-{360}^{°}$ or,

Convert the degree measure to radians. For this, multiply by $\frac{\pi }{{180}^{°}}$ .

  $\begin{array}{c}{105.24}^{°}={105.24}^{°}.\frac{\pi }{{180}^{°}}\\ =\frac{{105.24}^{°}.\pi }{{180}^{°}}\\ \approx 1.84\end{array}$

Therefore, the measure of the angle between $0$ and $2\pi$ that is conterminal with $\alpha$ is about $1.84$ radians.