A circle C of radius 2r has its center at the origin. A circle of radius r rolls without slipping in the counterclockwise direction around C. A point P is located on a fixed radius of the rolling circle at a distance b from its center, 0<b<r. Let L be the line from the center of C to the center of the rolling circle and t be the angle that L makes with the positive x-axis. Parametric equations of the path traced out by P are x(t) = 3r cos t + b cos 3t and y(t) = 3r sin t + b sin 3t Show that an equilateral triangle can be inscribed in the epitrochoid and that its centroid is on a circle of radius b centered at the center of the epitrochoid.
A circle C of radius 2r has its center at the origin. A circle of radius r rolls without slipping in the counterclockwise direction around C. A point P is located on a fixed radius of the rolling circle at a distance b from its center, 0<b<r. Let L be the line from the center of C to the center of the rolling circle and t be the angle that L makes with the positive x-axis. Parametric equations of the path traced out by P are x(t) = 3r cos t + b cos 3t and y(t) = 3r sin t + b sin 3t Show that an equilateral triangle can be inscribed in the epitrochoid and that its centroid is on a circle of radius b centered at the center of the epitrochoid.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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A circle C of radius 2r has its center at the origin. A circle of radius r rolls without slipping in the counterclockwise direction around C. A point P is located on a fixed radius of the rolling circle at a distance b from its center, 0<b<r. Let L be the line from the center of C to the center of the rolling circle and t be the angle that L makes with the positive x-axis.
Parametric equations of the path traced out by P are
x(t) = 3r cos t + b cos 3t and y(t) = 3r sin t + b sin 3t
Show that an equilateral triangle can be inscribed in the epitrochoid and that its centroid is on a circle of radius b centered at the center of the epitrochoid.
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