Question

Find the principal solutions of \( \cot \theta = 0 \)

Hint:

Principal solutions for trigonometric equations are within one cycle, typically \( [0, 2\pi) \).

Answer 1

\[ \cot \theta = \frac{\cos \theta}{\sin \theta} = 0 \Rightarrow \cos \theta = 0. \] \[ \cos \theta = 0 \text{at} \theta = \frac{\pi}{2} + n\pi, n \in \mathbb{Z}. \] Principal solutions are within \( [0, 2\pi) \): 
- \( n = 0 \): \( \theta = \frac{\pi}{2} \). 
- \( n = 1 \): \( \theta = \frac{\pi}{2} + \pi = \frac{3\pi}{2} \). 
Answer: \( \frac{\pi}{2}, \frac{3\pi}{2} \).