   Chapter 10.1, Problem 20E

Chapter
Section
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=x2 (1)

The parametric equation for x is as below.

y=1+3cost

cost=y13 (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(x2)2+(y13)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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