Help with 2 trigonometic equations?

Quote:

Solve the equation $\displaystyle \sin {2x} + \cos {3x} = 0$ for $\displaystyle [0, 2\pi)$.

**I know most of the trigonometric identies, but I'm still stuck on how to solve it.**

This is how far I've gotten.

$\displaystyle 2\sin{x}\cos{x} + \cos{(x+2x)}$

$\displaystyle 2\sin{x}\cos{x} + \cos{x}\cos{2x} - \sin{x}\sin{2x}$

**Help?**

Quote:

Solve the equation $\displaystyle \cos{2x} - \sin{x} = \frac {1}{2}$ for $\displaystyle [0, 2\pi)$

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**Same problem here. I get stuck and can't solve the problem. Help?**