Question

Rewrite each degree measure in radians and each radian measure in degrees if the angle is $-225°$.

Short answer

The degree measure in radians of angle $-225°$ is $-\frac{5\pi }{4}\text{rad}$.

Step-by-step solution

Step 1. Write down the given information.

The given angle in degrees measure is$-225°$.

Step 2. Concept used.

From the degree – radian conversion rule.

$\pi \text{Radian}=180{}^{\circ }....\left(1\right)$

Step 3. Convert degrees measures to radians.

The angle $-225°$in radian units is evaluated with the help of concept (1) stated above.

$\begin{array}{l}-{225}^{°}=-{225}^{°}\times \frac{\pi }{{180}^{°}}\text{rad}\\ =-\frac{5\pi }{4}\text{rad}\end{array}$

Step 4. Conclusion.

The degree measure in radians of angle $-225°$is $-\frac{5\pi }{4}\text{rad}$.