Problem

Describe the motion of a particle with position $…

02:56

Problem 20 Easy Difficulty

Describe the motion of a particle with position $ (x, y) $ as $ t $ varies in a given interval.

$ x = 2 + \sin t $, $ \; y = 1 + 3\cos t $, $ \; \pi/2 \leqslant t \leqslant 2\pi $

Answer

The particle starts at $(3,1)$ then moves 3$/ 4$ of the way around clockwise on the path of an ellipse with center at $(2,1),$ ending at $(2,4)$

Topics

Parametric Equations

Polar Coordinates

Calculus: Early Transcendentals

Chapter 10

Parametric Equations and Polar Coordinates

Section 1

Curves Defined by Parametric Equations

Discussion

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Video Transcript

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