Question

The position of a particle moving in the xy plane is given by r⃗ =2.0cos(3.0rad/st)i^+2.0sin(3.0rad/st)j^, where r is in meters and t is in seconds.

Show that this represents circular motion of radius 2.0 m centered at the origin.

Answer 1

Write it like parametric equations, like this (also, don't write rad/s etc in there, makes it look way more confusing)

x = 2cos3t
y = 2sin3t

from those you get x/2 = cos3t and y/2 = sin3t

Now use the fact that \[\Large \cos^2 \theta +\sin^2 \theta = 1\]

Answer 2

You will want to square both sides of each of these:

x/2 = cos3t
and
y/2 = sin3t

Answer 3

Thank you. That is actually how we were given the question in MasteringPhysics. That have been where some of my confusion came from.