Use the picture below to explain why

Hence, solve the equations

1. $$3{\sin }^2(\theta )+{\cos }^2(\theta )=2$$
2. $$2{\cos }^2(\theta )-3{\sin }^2(\theta )=1$$

giving all solutions $\theta$ satisfying $0\le \theta \le 360.$

By definition,

so $y=\sin (\theta ).$ Do similar for $\cos (\theta )$ and then use Pythagoras.

Since ${\sin }^2(\theta )+{\cos }^2(\theta )=1,$ we can say that ${\cos }^2(\theta )=1-{\sin }^2(\theta ).$

So substitute ${\cos }^2(\theta )=1-{\sin }^2(\theta )$ into the equation, and now you only have $\sin$ in your equation, which will allow you to solve it!