How to use Double Angle Identity to solve sin(3x)?

Question

given sin(x) = (2√2)/3 cos(x)= -1/3

How would you solve sin(3x) using the formula:

#sin(3x)=sin(23/2x)=sin(23/2x)cos(2*3/2x)#

Thank you!

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Answer 1 · 2018-06-20T17:53:31

See my answer below!

#sin(3x)=sin(x+2x)=sin(x)cos(2x)+cos(x)sin(2x)#
Now use that
#sin(2x)=2sin(x)cos(x)#
#cos(2x)=cos^2(x)-sin^2(x)=1-2sin^2(x)#