If a string wound around a fixed circle is unwound while held taut in the plane of the circle, its end P traces an involute of the circle. In the accompanying figure, the circle in question is the circle (x^2)+(y^2)=1 and the tracing point starts at (1,0). The unwound portion of the string is tangent to the circle at Q, and t is the radian measure of the angle from the positive x-axis to segment OQ. Derive the parametric equations
x=cost+tsint, y=sint-tcost, t>0
of the point P(x,y) for the involute.
The Attempt at a Solution
I have no idea how to do this problem!! The section it's in is "Arc length and the unit-Tangent vector," but the only things explained in the section are arc length and unit tangent vector! I don't see how this relates... If anyone can provide a detailed explanation, I'd be grateful.