Question

find the reference angle for $\frac{6pi}{5}$. radians

Explanation:

Step1: Determine the quadrant

The angle $\theta=\frac{6\pi}{5}$ is between $\pi$ and $\frac{3\pi}{2}$ since $\pi=\frac{5\pi}{5}$ and $\frac{3\pi}{2}=\frac{15\pi}{10}>\frac{6\pi}{5}$. So it is in the third - quadrant.

Step2: Use the reference - angle formula for third - quadrant angles

For an angle $\theta$ in the third quadrant, the reference angle $\theta_{r}=\theta-\pi$.
$\theta_{r}=\frac{6\pi}{5}-\pi=\frac{6\pi - 5\pi}{5}=\frac{\pi}{5}$

Answer:

$\frac{\pi}{5}$