A merry-go-round is rotating at the constant angular speed of 3 RPM counterclockwise. The platform of this ride is a circular disk of radius 24

Question

feet.
(a) If θ = 34 degrees, what are your xy coordinates after 4 minutes?
(b) If θ = 20 degrees, what are your xy coordinates after 45 minutes?
(c) If θ = −14 degrees, what are your xy coordinates after 6 seconds?
(d) If θ = -2.1 rad, what are your xy coordinates after 2 hours and 7 seconds?

Answer 1

what does θ have to do with anything?
For (a), after 4 minutes, the wheel has turned 3 complete revolutions.

Answer 2

since a merry-go-round is circulur theta is the arc of the circle (there is an image but I can't upload it onto here). i thought that maybe you would have to use the parametric equation of a circle to find the xy coordinate but i am not 100% positive

Answer 3

well, I will say that if θ is the central angle, then the arc length (distance traveled at the rim) is s = rθ

Now, if you can make θ a function of time, s(t) = r θ(t). But since you have already said what the rotation speed is, the time will tell you what θ is.
after t minutes, θ = 360*3t degrees

Answer 4

how would that give you the xy coordinate?