calculus/Trig
posted by John on .
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:____

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