   Chapter 10.2, Problem 35E

Chapter
Section
Textbook Problem

# Conjecture(a) Use a graphing utility to graph the curves represented by the two sets of parametric equations.x = 4 cos ty = 3 sin tx = 4 cos(–t)y = 3 sin(–t)(b) Describe the change in the graph when the sign of the parameter is changed.(c) Make a conjecture about the change in the graph of parametric equations when the sign of the parameter is changed.(d) Test your conjecture with another set of parametric equations.

(a)

To determine

To graph: The curves, x=4cost,y=3sint and x=4cos(t),y=3sin(t).

Explanation

Given:

The equations of the curves, x=4cost,y=3sint and x=4cos(t),y=3sin(t).

Graph:

Consider the curve, x=4cost,y=3sint.

Use a graphing utility and plot the equation of the curve, x=4cost,y=3sint

So,

Now, consider the curve, x=4cos(t),y=3sin(t)

(b)

To determine

The description of the change in the graph in part (a) when the signs of the parameter is changed.

(c)

To determine

The conjecture when the signs of the parameter is changed in the parametric equations.

(d)

To determine

If the conjecture, made in part (c) is correct by another set of parametric equations.

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