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Chapter 9: Q. 14 (page 746)

Using polar coordinates, the graphs of the equationsr=cosk胃and r=sink胃are roses with k petals when k鈮�3is an odd integer. What are the polar graphs of these equations whenk=1? What are the graphs of these equations when k is a negative odd integer?

Short Answer

Expert verified

The graph of the curves is a circle when k=1

The graph of the curves is a roses having knumber of petals if kis a negative odd integers.

Step by step solution

01

Step 1. Given information

Polar curves:

r=cosk胃r=sink胃

k=1k鈮�3

02

Step 2. Graphs of curves when k=1.

When k=1then the graph of r=cos胃and graph of r=sin胃

03

Step 3. Graph of the curves when k is negative odd integers.

When kis negative odd integers then the graph of the given curves are also a rose having knumber of petals.

For example, if k=-5then graph of r=cos-5胃and r=sin-5胃are drawn as:

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