Questions: Find an angle between 0 and 2π that is coterminal with the given angle. 17π/6

Solution Steps

Coterminal angles are angles that have the same initial and terminal sides but differ by a multiple of \(2\pi\). To find a coterminal angle between \(0\) and \(2\pi\), we need to add or subtract \(2\pi\) from the given angle until the result lies within the desired range.

The given angle is \(\frac{17\pi}{6}\). First, express \(2\pi\) with a denominator of 6: \[ 2\pi = \frac{12\pi}{6} \] Now, subtract \(2\pi\) from the given angle: \[ \frac{17\pi}{6} - \frac{12\pi}{6} = \frac{5\pi}{6} \]

Check if \(\frac{5\pi}{6}\) lies between \(0\) and \(2\pi\): \[ 0 < \frac{5\pi}{6} < 2\pi \] Since \(\frac{5\pi}{6}\) is within the desired range, it is the coterminal angle we are looking for.

Final Answer