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Math
CalculusMultivariable Calculus8th Edition

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Chapter 10.1, Problem 20E
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Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643

Solutions

Chapter
Section
Problem 1E
Problem 2E
Problem 3E
Problem 4E
Problem 5E
Problem 6E
Problem 7E
Problem 8E
Problem 9E
Problem 10E
Problem 11E
Problem 12E
Problem 13E
Problem 14E
Problem 15E
Problem 16E
Problem 17E
Problem 18E
Problem 19E
Problem 20E
Problem 21E
Problem 22E
Problem 23E
Problem 24E
Problem 25E
Problem 26E
Problem 27E
Problem 28E
Problem 29E
Problem 30E
Problem 31E
Problem 32E
Problem 33E
Problem 34E
Problem 35E
Problem 36E
Problem 37E
Problem 38E
Problem 39E
Problem 40E
Problem 41E
Problem 42E
Problem 43E
Problem 44E
Problem 45E
Problem 46E
Problem 47E
Problem 48E
Problem 49E
Problem 50E
Problem 51E
Problem 52E
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Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643
Textbook Problem

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

20. x = 2 + sin t, y = 1 + 3 cos t, π/2 ≤ t ≤ 2π

To determine

The motion of a particle with position (x,y) as t varies.

Explanation

Given data:

The parametric equation for x is as below.

x=2+sint

sint=x−2 (1)

The parametric equation for x is as below.

y=1+3cost

cost=y−13 (2)

Here, t varies from π2 to 2π .

Calculation:

Squaring and adding both the equations (1) and (2) to obtain the motion of the particle .

sin2t+cos2t=1(x−2)2+(y−13)2=1

The value of t is increased from π2 to 2π with a step value of 1 and substituted in the parametric equations x=2+sint and y=1+3cost to obtain the value of x and y respectively

Determine the starting point (x1,y1) of the particle

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Chapter 10.1,
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Chapter 10.1,
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