Question

find the reference angle for $\frac{20pi}{9}$.

Explanation:

Step1: Find coterminal angle

First, find a coterminal angle of $\frac{20\pi}{9}$ that is between $0$ and $2\pi$. We know that $2\pi=\frac{18\pi}{9}$. So, $\frac{20\pi}{9}- 2\pi=\frac{20\pi}{9}-\frac{18\pi}{9}=\frac{2\pi}{9}$.

Step2: Determine reference - angle

Since $\frac{2\pi}{9}$ is in the first - quadrant (where $0\lt\theta\lt\frac{\pi}{2}$), the reference angle of an angle in the first - quadrant is the angle itself.

Answer:

$\frac{2\pi}{9}$