Question

find the reference angle for the angle $\frac{29pi}{3}$. the reference angle is (type your answer in radians. type an integer or a simplified fraction.)

Explanation:

Step1: Find a coterminal angle

Subtract \(2\pi\) (or \(\frac{6\pi}{3}\)) from \(\frac{29\pi}{3}\) multiple - times until the angle is between \(0\) and \(2\pi\). \(\frac{29\pi}{3}-4\times2\pi=\frac{29\pi}{3}-\frac{24\pi}{3}=\frac{5\pi}{3}\).

Step2: Determine the reference angle

The angle \(\frac{5\pi}{3}\) is in the fourth - quadrant. The reference angle \(\theta_{r}\) for an angle \(\theta\) in the fourth - quadrant is given by \(2\pi-\theta\) or \(\theta_{r} = 2\pi-\frac{5\pi}{3}=\frac{\pi}{3}\).

Answer:

\(\frac{\pi}{3}\)