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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.

39. r = 1 + 3 cos θ

To determine

To sketch: The curves for the given Cartesian and polar coordinates r=1+3cosθ .

Explanation

Given:

The polar equation is as below.

r=1+3cosθ .

Calculation:

Substitute (0) for θ in equation r=1+3cosθ .

r=1+3cosθ=1+3cos(0)=1+3=4

For the polar equation r=1+3cosθ values for the Cartesian coordinates curve is tabulated below.

θ

(degrees)

θ

(rad)

r
0 0 4
10 0.174611111 3.954382519
20 0.349222222 3.818917381
30 0.523833333 3.597724303
40 0.698444444 3.297530134

The curve for the Cartesian coordinates is shown below in figure1

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