Chapter 4, Problem 12RE

To determine

To Convert: Angle measure from degrees to radians.

Answer to Problem 12RE

The radian measure is $3.927$ radians.

Explanation of Solution

Given information:

The degree measure is ${225}^{\circ }$

Formula used:

The relation between degree measure and radian is given

Mathematically,

  $\begin{array}{l}{360}^{\circ }=2\pi \text{radians}\\ {180}^{\circ }=\pi \text{radians}\\ 1^{\circ }=\frac{\pi }{180}\text{radians}\end{array}$

Calculation:

The degree measure is

  $\begin{array}{l}{360}^{\circ }=2\pi \text{ radians}\\ {180}^{\circ }=\pi \text{ radians}\\ 1^{\circ }=\frac{\pi }{180}\text{ radians}\\ {225}^{\circ }=\left(225\times \frac{\pi }{180}\right)\text{ radians}=\frac{5\pi }{4}\text{ radians}=3.927\text{ radians}\\ \end{array}$

Therefore, the radian measure is $3.927$ radians.