Help With Simple Harmonic Motion?

Question

A particle executes simple harmonic motion with an amplitude of 6.00 cm. At what positions does its speed equal one third of its maximum speed?

a) larger number __________

b) smaller number ___________

Answer 1

so the displacement of the particle is 6 sin (w t)

speed of particle = 6 w cos ( w t)

Maximum speed is 6 w  when t=0

one third speed is when cos (wt) = 1/3

so displacement = +- 6 sin ( inverse cos 1/3 )