Question

What is $\frac{3\mathrm{\pi }}{4}$ in degrees?

Answer 1

Finding degree measure of a given radian measure of an angle:

It is known that $2\mathrm{\pi }\mathrm{radians}$ is equal to $360°$.

So, $x\mathrm{radians}$ is equal to $\frac{x·360}{2\mathrm{\pi }}=\frac{180x}{\mathrm{\pi }}\mathrm{degrees}$.

Hence, for $\frac{3\mathrm{\pi }}{4}\mathrm{radians}$:

$\frac{180·3\mathrm{\pi }}{\mathrm{\pi }·4}=135°$

Therefore, the degree measure of the given radian measure of the angle, $\frac{\mathbf{3}\mathbf{\pi }}{\mathbf{4}}\mathbf{=}\mathbf{135}\mathbf{°}$.