Question

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

Answer 1

by solve i mean distribute

Answer 2

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

Answer 3

\(\bf [3cos(3\theta)]^2\implies 3^2[cos(3\theta)]^2\implies 9cos^2(3\theta)
\\ \quad \\
\textit{triple angle identity}\to{\color{brown}{ cos^3(\theta)= 4cos^3(\theta)-3cos(\theta)}}
\\ \quad \\
9cos^2(3\theta)\implies 9[4cos^3(\theta)-3cos(\theta)]^2\)

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

Answer 4

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

Answer 5

supposed to be r=3cos(3theta)