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Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643
Textbook Problem

Use a graphing device to graph the polar curve. Choose the parameter interval to make sure that you produce the entire curve.

67. r = 1 + 2 sin(θ/2) (nephroid of Freeth)

To determine

To find: The parameter interval to plot Nephroid of freeth for the polar equation r=1+2sinθ2 .

Explanation

Given:

The polar equation is r=1+2sinθ2 .

Calculation:

The equation for the variable x is given below,

x=rcosθ

The equation for the variable y is given below,

y=rsinθ

Substitute (1+2sinθ2) for r in equation x=rcosθ ,

x=rcosθ=(1+2sinθ2)cosθ

Substitute (1+2sinθ2) for r in equation y=rsinθ ,

y=rsinθ=(1+2sinθ2)sinθ

Substitute (0) for θ in equation (1+2sinθ2) ,

x=(1+2sinθ2)cosθ=1+2sin(0)2cos(0

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