   Chapter 10.1, Problem 21E

Chapter
Section
Textbook Problem

# Describe the motion of a particle with position (x, y) as t varies in the given interval.21. x = 5 sin t, y = 2 cos t, −π ≤ t ≤ 5π

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=5sint

sint=x5 (1)

Write the parametric equation for y

y=2cost

cost=y2 (2)

Here, t varies from π to 5π

Calculation:

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

sin2t+cos2t=1(x5)2+(y2)2=1

The value of t is increased from π to 5π with a step value of 1 and substituted in the parametric equations x=5sint and y=2cost to obtain the value of x and y respectively.

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

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