Question

find the reference angle for the angle -\frac{47\pi}{6}. the reference angle is . (type your answer in radians. type an integer or a simplified fraction.)

Explanation:

Step1: Make the angle positive

Add \(2k\pi\) (\(k\in\mathbb{Z}\)) to make the angle positive. Let's find \(k\) such that \(-\frac{47\pi}{6}+ 2k\pi>0\).
\(-\frac{47\pi}{6}+2k\pi=\frac{- 47\pi + 12k\pi}{6}>0\), we want \(-47 + 12k>0\), \(12k>47\), \(k = 4\).
\(-\frac{47\pi}{6}+8\pi=-\frac{47\pi}{6}+\frac{48\pi}{6}=\frac{\pi}{6}\)

Answer:

\(\frac{\pi}{6}\)