   Chapter 10.1, Problem 19E

Chapter
Section
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)

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started 