Question

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

Answer 1

Determine the reference angle for $240°$ in degrees and radians:

The angle $240°$ lies between $180°$ and $270°$, which means that it lies in the third quadrant. Recall that for an angle $\theta$ in the third quadrant such that $180°<\theta \le 270°$, the reference angle is given by $\theta -180°$. Thus, the reference angle for $240°$ is $240°-180°=60°$. Recall that to convert a degree measure angle to a radian measure angle, it is multiplied by the conversion factor $\frac{\mathrm{\pi }}{180°}$.

Thus, the angle $60°$ can be represented in radians as $60°\times \frac{\mathrm{\pi }}{180°}=\frac{\mathrm{\pi }}{3}\text{radians}$.

Hence, the reference angle for $240°$ is $\mathbf{60}\mathbf{°}$ or $\frac{\mathbf{\pi }}{\mathbf{3}}\mathbf{}\mathbf{\text{radians}}$.