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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.

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. the circle in question is 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 parametric equations for the involute by expressing the coordinates x and y of P in terms of t for t greater and equal to zero.

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