Question

Suppose you wish to express sin(3t) in terms of sint and cost. Apply the sum formula to sin(3t) = sin(t+2t) to obtain an expression that contains sin(2t)=sin(t+t) and cos(2t)=cos(t+t). Apply the sum formulas to those two expressions. Enter the resulting expression for sin(3t) here:____

Answer 1

sin(3t) = sin(2t)cos t + sint cos(2t)
= [2sint*cos^2t + sint(cos^2t - sin^2t)
= 3sint*cos^2t -sin^3t
You can get rid of the cosine function.
= 3sint(1 - sin^2t)- sin^3t
= 3sint -4 sin^3t