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x = sin(t/2), y = sin(t)

x = sin(t/2), y = sin(t)

Calculus: Early Transcendentals
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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Question
2. Bowditch curve The Bowditch curve is defined by the parametric equations x = sin(t/2), y = sin(t) It is a closed curve meaning it begins to repeat itself as t gets larger and larger. %3D a. Starting with t= 0, determine the first t-value greater than 0 such that the curve begins to repeat itself. b. Find an equation for the tangent line when t= 0. c. From the above plot, it is clear there are four points on this curve where the curve has ntal tangents. Find t-values for these four points and then give the (x, y) coordinates for these points. d. There are two points on this curve where the curve has vertical tangents. Find t-values for these two points and then give the (x, y) coordinates for these points. e. Calculate the length of this curve. (Use technology to compute any integrals.)
Transcribed Image Text:2. Bowditch curve The Bowditch curve is defined by the parametric equations x = sin(t/2), y = sin(t) It is a closed curve meaning it begins to repeat itself as t gets larger and larger. %3D a. Starting with t= 0, determine the first t-value greater than 0 such that the curve begins to repeat itself. b. Find an equation for the tangent line when t= 0. c. From the above plot, it is clear there are four points on this curve where the curve has ntal tangents. Find t-values for these four points and then give the (x, y) coordinates for these points. d. There are two points on this curve where the curve has vertical tangents. Find t-values for these two points and then give the (x, y) coordinates for these points. e. Calculate the length of this curve. (Use technology to compute any integrals.)
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