Use the diagram to explain why

Hence, solve the following for all values of $\theta$ such that $-180\le \theta \le 180.$

1. $$3\sin (\theta )=2\cos (\theta )$$
2. $$\sqrt{5}\sin (\theta )+2\cos (\theta )=0$$
3. $$\frac{1}{\sin (\theta )}-\frac{\sqrt{3}}{\cos (\theta )}=0$$

In (a) and (b), you can divide by $\cos (\theta )$, and then make use of the fact that

In (c), you can multiply by $\sin (\theta )$ to make $\frac{\sin (\theta )}{\cos (\theta )}$