   Chapter 10.3, Problem 41E

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.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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