When a circle rolls on the inside of a fixed circle, any point P on the circumference

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When a circle rolls on the inside of a fixed circle, any point P on the circumference of the rolling circle describes a hypocycloid. Let the fixed circle be x2 + y2 = a2, let the radius of the rolling circle be b, and let the initial position of the tracing point P be A(a, 0). Find parametric equations for the hypocycloid, using as the parameter the angle θ from the positive x-axis to the line joining the circles’ centers. In particular, if b = a/4, as in the accompanying figure, show that the hypocycloid is the astroidimage

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Thomas Calculus Early Transcendentals

ISBN: 9780321884077

13th Edition

Authors: Joel R Hass, Christopher E Heil, Maurice D Weir

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