If a string wound around a fixed circle is unwounded while held taught in the plane of the circle, its end P traces an involute of the circle. In the attached figure, the circle in the question is the

INVOLUTE OF A CIRCLE :If a string wound around a fixed circle is unwounded while held taught in the plane of the circle, its end P traces an involute of the circle. In the attached figure, the circle in the 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. Find the parametric equations of the point P(x,y) for the involute.