physics
posted by Hannah .
A particle moves in a circle in such a way that the x and ycoordinates of its motion are given in meters as functions of time t in seconds by:
x=5cos(3t)
y=5sin(3t)
What is the period of revolution of the particle?
Here's what my train of thought was... dy/dt over dx/dt would equal dy/dx which equals velocity. So velocity would be cot(3t). But then how do I find r? Plus none of the answers here have a trig function in them... ???????

Hmmmm. You are not asked for r, you are asked for period, in time.
3t= 2PI*n n=0, 1, ...
t= 2/3 PI n try n=1 for the first rev. 
I was looking for r because period = [2(pi)(r)]/v......
And how did you get to 3t=2Pi*n???? What equation is that????? 
solve t by the method I gave, for get r.
3t=0, 2PI, 4PI....is not the period of a sin function =2PI or a multiple thereof? 
Well, just think about it logically: if the equation were x=5cos(t) and y=5sin(t), then the period of revolution (time for it to complete one cycle) would be 2 pi, because that's the period of the sin/cos function. However, since it's 3t instead of t, the cycle of rotation would be much faster: set 3t=2*pi, so t, or the new period of revolution, is 2*pi/3.
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