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Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643

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BuyFindarrow_forward

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.

19. x = 5 + 2 cos πt, y = 3 + 2 sin πt, 1 ≤ t ≤ 2

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=5+2cosπt

cosπt=x52 (1)

The parametric equation for x is as below.

y=3+2sinπt

sinπt=y32 (2)

Here, t varies from 1 to 2 .

Calculation:

Squaring and adding Equations (1) and (2) ,

cos2(πt)+sin2(πt)=1(x52)2+(y32)2=1

The value of t is increased from 1 to 2 with a step value of 1 and substituted in the parametric equations x=5+2cosπt and y=3+2sinπt to obtain the value of x and y , respectively.

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

Substitute 1 for t in Equation (1)

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Chapter 10 Solutions

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P-52RECh-10 P-53RECh-10 P-54RECh-10 P-55RECh-10 P-56RECh-10 P-57RECh-10 P-58RECh-10 P-1PCh-10 P-2PCh-10 P-3PCh-10 P-4PCh-10 P-5PCh-10 P-6P

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