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Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643
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.

34. r = θ2, −2πθ ≤ 2π

To determine

To sketch: The curves for the polar equation r=θ2 and its Cartesian coordinates.

Explanation

Given:

The polar equation is as below.

r=θ2 .

Calculation:

Substitute (12.572) for θ in equation r=θ2 .

r=θ2=(12.572)2=158.05

For the polar equation r=θ2 values for the Cartesian coordinates curve is tabulated below.

θ

(degrees)

θ

(rad)

r
–720 –12.572 158.05518
–710 –12.39738889 153.69525
–700 –12.22277778 149.3963
–690 –12.04816667 145.15832
–680 –11.87355556 140.98132

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

From the figure 1 , when θ increases from 2π to 1

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