A particle travels on a curve given parametrically by (cos(2t), sin(3t)) where t is in seconds. Describe the motion of the particle on the interval [0,3] When does the particle first cross the y-axis? Set up a trigonometric equation and solve for t exactly. When does the particle first change direction? Find the exact a. b. C. value for t. d. e. f. Find the speed of the particle at t = 1 second Find the slope of the tangent line to the parametric curve at t = 4 seconds. Find a parametric representation of the tangent line (ray) at t = 4 seconds.

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 particle travels on a curve given parametrically by (cos(2t), sin(3t))
where t is in seconds.
Describe the motion of the particle on the interval [0,3]
When does the particle first cross the y-axis? Set up a
trigonometric equation and solve for t exactly.
When does the particle first change direction? Find the exact
a.
b.
C.
value for t.
d.
e.
Find the speed of the particle at t = 1 second
Find the slope of the tangent line to the parametric curve at t = 4
seconds.
Find a parametric representation of the tangent line (ray) at t = 4
seconds.
Transcribed Image Text:A particle travels on a curve given parametrically by (cos(2t), sin(3t)) where t is in seconds. Describe the motion of the particle on the interval [0,3] When does the particle first cross the y-axis? Set up a trigonometric equation and solve for t exactly. When does the particle first change direction? Find the exact a. b. C. value for t. d. e. Find the speed of the particle at t = 1 second Find the slope of the tangent line to the parametric curve at t = 4 seconds. Find a parametric representation of the tangent line (ray) at t = 4 seconds.
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