**Question:**Give the exact value of \( \cot \left( \frac{17\pi}{6} \right) \).**Explanation:**This question asks for the exact value of the cotangent function evaluated at the angle \( \frac{17\pi}{6} \). To solve this, follow these steps:1. Simplify the angle \( \frac{17\pi}{6} \): Since angles in trigonometry can be coterminal, \( \frac{17\pi}{6} \) can be reduced within one full circle (or \( 2\pi \)). \[ \frac{17\pi}{6} = \frac{17}{6} \pi \] Subtract \( 2\pi \) (since one full circle is \( 2\pi \)): \[ \frac{17}{6}\pi - 2\pi = \frac{17\pi - 12\pi}{6} = \frac{5\pi}{6} \] This means that \( \frac{17\pi}{6} \) is coterminal with \( \frac{5\pi}{6} \).2. Evaluate \(\cot \left( \frac{5\pi}{6} \right) \): Cotangent is the reciprocal of tangent: \[ \cot \theta = \frac{1}{\tan \theta} \] For \(\theta = \frac{5\pi}{6} \): \[ \cot \left( \frac{5\pi}{6} \right) = \frac{1}{\tan \left( \frac{5\pi}{6} \right)} \] The tangent function of \( \frac{5\pi}{6} \) can be evaluated considering it is in the second quadrant: Tangent in the second quadrant: \[ \tan \left( \frac{5\pi}{6} \right) = - \tan \left( \pi - \frac{\pi}{6} \right) = - \tan \left( \frac{\pi}{6} \right) = - \frac{1}{\sqrt{3}} \] Hence: \[ \cot \left(

Name: **Question:**Give the exact value of \( \cot \left( \frac{17\pi}{6} \
Uploaded: 2024-03-20T06:46:55.000Z
Channel: Bartleby
Description: **Question:**Give the exact value of \( \cot \left( \frac{17\pi}{6} \right) \).**Explanation:**This question asks for the exact value of the cotangent function evaluated at the angle \( \frac{17\pi}{6} \). To solve this, follow these steps:1. Simpli