   Chapter 10.3, Problem 40E

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.40. r = 1 + 5 sin θ

To determine

To sketch: The curves for the given Cartesian and polar coordinates r=1+5sinθ .

Explanation

Given:

The polar equation is as below.

r=1+5sinθ .

Calculation:

Substitute (0) for θ in equation r=1+5sinθ .

r=1+5sinθ=1+5sin(0)=1

For the polar equation r=1+5sinθ values for the Cartesian coordinates curve is tabulated below.

 θ (degrees) θ (rad) r 0 0 1 10 0.174611111 1.868625876 20 0.349222222 2.710835403 30 0.523833333 3.501015596 40 0.698444444 4.215135769

The curve for the Cartesian coordinates is shown below in figure1

From the figure 1 θ increases from 0 to π2 . Polar curve r increases from 1 to 6 in polar graph

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