i asked this question before but didn't really get a particular answer.

Question

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
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

still no indication of what θ means. If it is the angle through which the wheel has rotated, then when θ=34°
(x,y) = (r cosθ, r sinθ) = (19.9,13.42)

But the rotation speed and time already tell you how far the wheel has gone, so who needs θ?

If θ is the angle when the rotation starts, then after a whole number of minutes, the wheel is back where it started. For
(c) the wheel has rotated 6/60 * 3 * 360 = 108° so add that to the initial value of -14°, so use 96° for your coordinates.

Once you decide what θ means for this problem, then it's just plug and chug. Until then, you're doomed.

Answer 2

If theta is measured counterclockwise from the x axis then
x= R cos theta and y = R sin theta

Answer 3

Maybe theta here is angle off horizontal ?