Plot the corresponding reference circle for each of the following simple harmonic motions. Indicate the initial (t = 0) position of the particle, the radius of the circle, and the angular speed of the rotating particle. For simplicity, the sense of rotation may be fixed to be anti-clockwise in every case:

(x is in cm and t is in s)
(a) x = - 2 sin (3t + ``\pi`` /3)
(b) x = cos (``\pi`` /6 - t)
(c) x = 3 sin (2``\pi``t + ``\pi`` /4)
(d) x = 2 cos ``\pi`` t.