Trigonometric Equations

1. Find all solutions of the given equation. Let $k$ be any integer.   solution

(a) \( \sin (\theta) = \frac{\sqrt{3}}{2}\)      (b) \( \cos (\theta) = -\frac{1}{2}\)      (c) \( \tan (\theta) = 1\)

2. Find all solutions of the given equation. Let $k$ be any integer. List six specific solutions.  solution

(a) \( \sin (\theta) = \frac{\sqrt{2}}{2}\)     (b) \( \sqrt{2} \cos (\theta) + 1=0\)

3. Find all solutions of the given equation. Let $k$ be any integer.   solution

(a) \( \sin (\theta) \cos(\theta) - 5 \sin(\theta)=0 \)     (b) \( \tan^2(\theta) - 1 =0\)

4. Find all solutions of the given equation. Let $k$ be any integer.   solution

(a) \( 4\cos^2(\theta) -4 \cos(\theta) +1 = 0 \)     (b) \( 2\sin^2(\theta) - \sin(\theta)- 1 =0\)