Question

use reference angles to find the exact value of the following expression. do not use a calculator. determine the reference angle for $\frac{5pi}{3}$. the reference angle is $square$. (type your answer in radians. use integers or fractions for any numbers in the expression. type an exact answer, using $pi$ as needed.)

Explanation:

Step1: Determine the quadrant

The angle $\theta=\frac{5\pi}{3}$ is in the fourth - quadrant since $ \frac{3\pi}{2}<\frac{5\pi}{3}<2\pi$.

Step2: Calculate the reference angle

For an angle $\theta$ in the fourth - quadrant, the reference angle $\theta_{r}=2\pi-\theta$. Substitute $\theta = \frac{5\pi}{3}$ into the formula: $\theta_{r}=2\pi-\frac{5\pi}{3}=\frac{6\pi - 5\pi}{3}=\frac{\pi}{3}$.

Answer:

$\frac{\pi}{3}$