how would i solve (3cos(3theta))^2

Question

anonymous · Answer

by solve i mean distribute

anonymous · Answer

i know 3^2=9
but not sure how to handle cos(3theta) what do i do with the 3theta?

jdoe0001 · Answer

$\bf [3cos(3\theta)]^2\implies 3^2[cos(3\theta)]^2\implies 9cos^2(3\theta)
\ \quad \
\textit{triple angle identity}\to{\color{brown}{   cos^3(\theta)= 4cos^3(\theta)-3cos(\theta)}}
\ \quad \
9cos^2(3\theta)\implies 9[4cos^3(\theta)-3cos(\theta)]^2$

is what I can see thus far

if you're just distributing, well.. you can just expand that like you would any perfect square trinomial

anonymous · Answer

@jdoe0001 it is actually part of a a problem im having. finding area of a polar equation. 
r=3cos(3\Theta)

anonymous · Answer

supposed to be r=3cos(3theta)