Deriving Centripetal Acceleration

[Pupil]

Hi. I'm trying to derive a = (v^2)/r from the position of a particle moving in a circle. Since the equation for a particle moving in a circle is x(t) = r(isin(wt) + jcos(wt)) where w is constant. I took two derivatives to find it's acceleration. I got a(t) = -rw^2(icos(wt)+jsin(wt)). Now I'm stuck. How the heck and I getting rid of those trig functions? Thanks.

-Dan

 

[atyy]

Find the magnitude of the vector a. You will get i.icos^2+j.jsin^2. Then i.i is unit vector dotted with itself equals 1. Then sin^2+cos^2 is some trig identity.