   Chapter 10.3, Problem 39E

Chapter
Section
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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