Question

find the reference angle for $\frac{9pi}{5}$. the reference angle is (simplify your answer. use integers or fractions for any numbers in the expression. type your

Explanation:

Step1: Determine the quadrant

Since \(2\pi=\frac{10\pi}{5}\) and \(\frac{8\pi}{5}<\frac{9\pi}{5}<\frac{10\pi}{5}\), \(\frac{9\pi}{5}\) is in the fourth - quadrant.

Step2: Calculate the reference angle

For an angle \(\theta\) in the fourth - quadrant, the reference angle \(\theta_{r}=2\pi-\theta\). Here \(\theta = \frac{9\pi}{5}\), so \(\theta_{r}=\frac{10\pi}{5}-\frac{9\pi}{5}=\frac{\pi}{5}\).

Answer:

\(\frac{\pi}{5}\)