Your equation is of the form .
Assuming k is an integer. This always yields a
"We suppose that the wheel rolls to the right. P being at the origin when the turn angle t equals 0. The figure shows the wheel after it has turned t radians. The base of the wheel is at distance at from the origin. The wheel's center is at (at,a), and the coordinates of P are
To express in terms of t, we absorve that for some integer k, so
I get everything up to the prior line. How does that equal -sint?