(Continuation of Exercise 19. ) Find the unit tangent

Chapter 12, Problem 20E

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(Continuation of Exercise 19. ) Find the unit tangent vector to the involute of the circle at the point P(x, y).19. The involute of a 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. In the accompanying figure, the circle in question is the circle x2 + y2 = 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 of the point P(x, y) for the involute.

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