   Chapter 10, Problem 17PS

Chapter
Section
Textbook Problem

# Graphing Polar Equations Use a graphing utility to graph the polar equation r cos 5 θ + n cos θ for 0 ≤ θ < π and for the integers n = − 5 to n = 5 . What values of n produce the “heart” portion of the curve? What values of n produce the “bell” portion? (This curve, created by Michael W. Chamberlin, appeared in The College Mathematics Journal.)

To determine

To graph: The polar curve r=cos5θ+ncosθ where 0<θ<π for n=5 to n=5.

Explanation

Given: The polar curve r=cos5θ+ncosθ where 0<θ<π for n=5 to n=5.

Graph:

For n=5,r=cos5θ5cosθ.

Use the Ti-83 calculator to graph the function.

Step 1: Press the [MODE] key and the select the Polar curve option.

Step 2: Press the [Y=] key and then enter the provided equation to the right of Y1.

Step 3: Press [WINDOW] and enter the following values.

0 for θMin

π for θMax

6 for Xmin

6 for Xmax

4 for Ymin

4 for Ymax.

Step 4: Press [GRAPH] to sketch the graph.

The following graph is obtained.

Similarly, obtain the graphs for all integer values of n from 4 to 5.

For n=4,

For n=3,

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