A particle has horizontal position (in meters) relative to its starting location given byp(t)=sin(2t)p(t)=sin(2t) not cos(2t)cos(2t)

sin(2t)=2sin(t)cos(t)sin(2t)=2sin(t)cos(t)

cos(2t)=cos2(t)sin2(t)cos(2t)=cos2(t)-sin2(t)

a) Rewrite p(t) using one of the double angle formulas, and then use the product rule to determine the derivative, p'(t).

b) Use the other double angle formula to simplify p'(t).

c) Show the steps in finding a time and position of the particle when its velocity equals 1 m/s. In other words, find a value of t and p(t) when p'(t) = 1.