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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.

45. r = sin(θ/2)

To determine

To sketch: The curves for the polar equation r=sin(θ2) and its Cartesian coordinates.

Explanation

Given:

The polar equation is as below.

r=sin(θ2) .

Calculation:

Substitute (0.0873) for θ in equation r=sin(θ2) .

r=sin(θ2)=sin((0)2)=0

For the polar equation r=sin(θ2) values for the Cartesian coordinates curve is tabulated below.

θ

(degrees)

θ

(rad)

r
0 0 0
10 0.174611111 0.087194687
20 0.349222222 0.173725175
30 0.523833333 0.258932326
40 0.698444444 0.342167081

The curve for the Cartesian coordinates is shown below in figure 1.

From the figure 1 , when θ increases from 0 to π , the polar curve r increases from 0 to 1 in polar graph

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