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Hypocycloid 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 0 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 astroid x = a cos 0, y = a sin³ 0. A(a, 0)

Hypocycloid 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 0 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 astroid x = a cos 0, y = a sin³ 0. A(a, 0)

Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter8: Polar Coordinates And Parametric Equations
Section8.4: Plane Curves And Parametric Equations
Problem 64E: Epicycloid If the circle C of Exercise 63 rolls on the outside of the larger circle, the curve...
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Hypocycloid 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 0 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 astroid x = a cos 0, y = a sin³ 0. A(a, 0)
Transcribed Image Text:Hypocycloid 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 0 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 astroid x = a cos 0, y = a sin³ 0. A(a, 0)
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