# How do you solve sin(3x)=-1 and find all exact general solutions?

How do you solve $\mathrm{sin}\left(3x\right)=-1$ and find all exact general solutions?
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Malcolm Flores
$\mathrm{sin}\left(3x\right)=-1\to 3x={\mathrm{sin}}^{-1}\left(-1\right)$
$3x=\frac{3\pi }{2}+2\pi n$
$x=\frac{\pi }{2}+\frac{2\pi n}{3}$
$x=\frac{3\pi +4\pi n}{6}$
Solve for x.
$\mathrm{cos}\left(2x\right)=-\frac{\sqrt{3}}{2}$
$\mathrm{tan}\left(4x\right)=-1$