Question

convert each angle in degrees to radians. Express your answer as a multiple of $\mathrm{\pi }$.

${135}^{\circ }$

Short answer

Thus,${135}^{\circ }=\frac{3\mathrm{\pi }}{4}radian.$

Step-by-step solution

Step 1. Given

Given angle to be converted

${135}^{\circ }$

Step 2. Concept

As $1degree=\frac{\mathrm{\pi }}{180}radian$.

Step 3. Calculation

We know

$$\begin{gathered} 1degree=\frac{\mathrm{\pi }}{180}radian \\ thus \\ {135}^{\circ }=135\left(\frac{\mathrm{\pi }}{180}\right) \\ =\frac{3\mathrm{\pi }}{4} \end{gathered}$$