Solve using identities

[for]

\(\displaystyle sin(3t)=\frac{\sqrt(3)}{2}\)

I have to solve using identities and I can't just take the arcsin of both sides.

So I know that.. \(\displaystyle sin(2t+t)\),

Can I do something like \(\displaystyle sin(2t)cos(t)+cos(2t)sin(t)\)

Then..

\(\displaystyle (2sin(t)cos(t)cos(t))+(1-2sin^2(t))(sin(t))\)

This is where I get lost.

 

[tkhunny]

What?

\(\displaystyle sin(x) = \frac{\sqrt{3}}{2} \implies x = \frac{\pi}{3}+2k\pi, \frac{2\pi}{3}+2k\pi\)

For k an integer.

When they give you standard values, you may as well use them.