Question

Show that cos(3theta) = cos^3(theta)-3 cos(theta)sin^2(theta) ... use this to find an equation in rectangular coordinates for the curve r= 4 cos (3theta)......

ANY HELP ? ...?

Answer 1

First, the angle sum forumlas:sin(α+β)=sinαcosβ+sinβcosαcos(α+β)=cosαcosβ−sinαsinβSo,cos(3θ)=cos(2θ+θ)=cos(2θ)cosθ−sin(2θ)sinθ=(cos2θ−sin2θ)cosθ−(2sinθcosθ)sinθ
From there, it's distribute and simplify...