Question: A string is wound around a circle and then unwound while being held taut. The curve traced by the point P at the end of

A string is wound around a circle and then unwound while being held taut. The curve traced by the point P at the end of the string is called the involutes of the circle. If the circle has radius and center O and the initial position of P is (r, 0) and if the parameter is chosen as in the figure, show that parametric equations of the involutes are

x = r(cos 0 + 0 sin 0) y = r(sin 0 - 0 cos 8) T.

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