Question

find the reference angle for $\frac{4pi}{3}$. the reference angle is . (simplify your answer. use integers or fractions for any numbers in the expression. type your answer in radians.)

Explanation:

Step1: Determine the quadrant

The angle $\theta=\frac{4\pi}{3}$ is in the third - quadrant since $\pi<\frac{4\pi}{3}<\frac{3\pi}{2}$.

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

For an angle $\theta$ in the third quadrant, the reference angle $\theta_{r}=\theta - \pi$.
So, $\theta_{r}=\frac{4\pi}{3}-\pi=\frac{4\pi - 3\pi}{3}=\frac{\pi}{3}$.

Answer:

$\frac{\pi}{3}$