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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336

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BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336
Textbook Problem

Sketch the curve with the given polar equation by first sketching the graph of r as a function of θ in Cartesian coordinates.

35. r = 3 cos 3θ

To determine

To sketch: The curve for the polar equation r=3cos3θ and its Cartesian coordinates.

Explanation

Calculation:

The polar equation is r=3cos3θ.

Substitute (0) for θ in equation r=3cos3θ,

r=3cos3θ=3cos3(0)=3

For the polar equation r=3cos3θ values for the Cartesian coordinates curve is tabulated below.

θr
03
π60
π33
π20
2π33
5π60
π3
7π60
4π33
3π20
5π33
11π60
2π3

The curve for the Cartesian coordinates is shown below in Figure 1.

From Figure 1, it is observed that when θ increases from 0 to π6, the polar curve r decreases from 3 to 0 in the polar graph.

It is observed that when θ increases from π6 to π3, the polar curve r decreases from 0 to 3

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