Chapter 13.1, Problem 57WE

To determine

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

Answer to Problem 57WE

The measure of the angle between $0$ and $2\pi$ that is coterminal with $\alpha$ is about $3.28$ radians.

Explanation of Solution

Given information:

Given measure is $\alpha =-3$ .

Calculation:

Rewrite $\alpha$ in terms of degrees. For this, multiply by $\frac{{180}^{°}}{\pi }$ .

  $\begin{array}{c}-3=\left(-3\right).\frac{{180}^{°}}{\pi }\\ \approx -{171.90}^{°}\end{array}$

Next, find the angle that is coterminal with $\alpha$ .

The positive coterminal will be $-{171.90}^{°}+{360}^{°}$ or ${188.1}^{°}$ .

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

  $\begin{array}{c}{188.1}^{°}=\mathrm{188.1.}\frac{\pi }{{180}^{°}}\\ \approx 3.28\end{array}$ radians.

Therefore, the measure of the angle between $0$ and $2\pi$ that is coterminal with $\alpha$ is about $3.28$ radians.