Question

find the angle between 0 and 2π in radians that is coterminal to the given angle. -\frac{17}{6}\pi

Explanation:

Step1: Add \(2\pi\) to the given angle

To find a coterminal angle, we add \(2\pi\) (since \(2\pi\) is the period for angles in radians).
Let \(\theta =-\frac{17}{6}\pi\). We add \(2\pi\) multiple times. First, \(2\pi=\frac{12}{6}\pi\).
\(-\frac{17}{6}\pi + 2\pi=-\frac{17}{6}\pi+\frac{12}{6}\pi=-\frac{5}{6}\pi\)

Step2: Add \(2\pi\) again

Since \(-\frac{5}{6}\pi<0\), we add \(2\pi\) (or \(\frac{12}{6}\pi\)) again.
\(-\frac{5}{6}\pi+2\pi=-\frac{5}{6}\pi+\frac{12}{6}\pi=\frac{- 5 + 12}{6}\pi=\frac{7}{6}\pi\)

Answer:

\(\frac{7}{6}\pi\)