   Chapter 10.3, Problem 60E

Chapter
Section
Textbook Problem

# Writing(a) Each set of parametric equations represents the motionof a particle. Use a graphing utility to graph each setFirst Particle: x = 3 cos t , y = 4 sin t , 0 ≤ t ≤ 2 π Second Particle: x = 4 sin t , y = 3 cos t , . 0 ≤ t ≤ 2 π (b) Determine the number of points of intersection.(c) Will the particles ever be at the same place at the same time? If so. identify the point(s).

(a)

To determine

To-graph: The parametric equation x=3cost and y=4sint over the interval [0,2π] and the parametric equation x=4sint and y=3cost over the interval [0,2π] by the use of graphing utility.

Explanation

Given:

First set of parametric equations are x=3cost and y=4sint over the interval [0,2π].

And, the second set of parametric equations are x=4sint and y=3cost over the interval [0,2π]

(b)

To determine
The number of points of intersection of the graph of two parametric equation in part (a).

(c)

To determine

To calculate: whether the particles on the graphs of the equations in part (a) ever be at the same place at the same time. If so, identify the points.

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