   Chapter 10.3, Problem 43E

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.43. r = 2 + sin 3θ

To determine

To sketch: The curves for the given Cartesian and polar coordinates r=2+sin3θ .

Explanation

Given:

The polar equation is as below.

r=2+sin3θ .

Calculation:

Calculation:

Substitute (0) for θ in equation r=2+sin3θ .

r=2+sin3θ=2+sin3(0)=2

For the polar equation r=2+sin3θ values for the Cartesian coordinates curve is tabulated below.

 θ (degrees) θ (rad) r 0 0 2 10 0.174611111 2.500203119 20 0.349222222 2.866259866 30 0.523833333 2.999999752 40 0.698444444 2.865555907

The curve for the Cartesian coordinates is shown below in figure1

From the figure 1, when θ increases from 0 to π6 , polar curve r increases from 2 to 3 in polar graph.

When θ increases from π6 to π2 , polar curve r decreases from 3 to 1

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