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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.

41. r2 = 9 sin 2θ

To determine

To sketch: The curves for the given Cartesian and polar coordinates r2=9sin2θ .

Explanation

Given:

The polar equation is as below.

r2=9sin2θ .

Calculation:

Substitute (0) for θ in equation r2=9sin2θ .

r=9sin2θ=9sin2(0)=0

For the polar equation r2=9sin2θ values for the Cartesian coordinates curve is tabulated below.

θ

(degrees)

θ

(rad)

r
0 0 0
10 0.174611111 1.754851482
20 0.349222222 2.405669217
30 0.523833333 2.792192471
40 0.698444444 2.977288292

The curve for the Cartesian coordinates is shown below in figure1

From the figure 1, when θ increases from 0 to π4 , polar curve r increases from 0 to 3 in polar graph

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P-52RECh-10 P-53RECh-10 P-54RECh-10 P-55RECh-10 P-56RECh-10 P-57RECh-10 P-58RECh-10 P-1PCh-10 P-2PCh-10 P-3PCh-10 P-4PCh-10 P-5PCh-10 P-6P

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