Question

What is the reference angle for $240°$? Put your answer in degrees and in radians

Answer 1

Step 1: Find the reference angle for $240°$:

Reference Angle: The acute angle between the terminal arm/terminal side and the $x-$axis. The reference angle is always positive. In other words, the reference angle is an angle sandwiched between the terminal side and the $x-$axis. It must be less than $90°$ and always positive.

Since the angle $180\mathrm{°}$ is in the third quadrant,

Subtracting $180\mathrm{°}$ from $240\mathrm{°}$,

$240°-180°=60°$

Step 2: Expressing $60°$ in radians:

$\begin{array}{rcl}360°& =& 2\mathrm{\pi }\mathrm{radians}\\ & \Rightarrow & 60°=\frac{2\mathrm{\pi }}{360}\times 60\\ & =& \frac{\mathrm{\pi }}{3}\mathrm{radians}\end{array}$

Therefore, the reference angle for $240\mathrm{°}$ is $60°$ and $\frac{\mathrm{\pi }}{3}\mathrm{radians}$.