Imagine a point on the edge of a circle. The circle rotates through this point as the pictures below show. Is there a formula that calculates the circle position given a specific angle?
2026-03-29 21:51:35.1774821095
Circle rotation along a point
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Welcome to Math.SE! Not sure what you mean by circle position, but let's assume the center of the original circle, which is the point of rotation, is in the origin of the coordinate system. Let's assume the circle we are rotating has radius $1$.
Thus, given an angle $t$ to the positive $x$-axis, the coordinate of the center of the rotated circle must be $(\cos t, \sin t)$, which makes the equation of the resulting circle $$ (x - \cos t)^2 + (y - \sin t)^2 = 1. $$
Can you do the case when circle has radius $r$?