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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.

69. r = esin θ − 2 cos(4θ) (butterfly curve)

To determine

To find: The parameter interval to plot butterfly curve for the polar equation r=esinθ2cos(4θ) .

Explanation

Given:

The polar equation is as below,

r=esinθ2cos(4θ)

Calculation:

The equation for the variable x is given below,

x=rcosθ

The equation for the variable y is given below,

y=rsinθ

Substitute (esinθ2cos(4θ)) for r in equation x=rcosθ ,

x=rcosθ=(esinθ2cos(4θ))cosθ

Substitute (esinθ2cos(4θ)) for r in equation y=rsinθ ,

y=rsinθ=(esinθ2cos(4θ))sinθ

Substitute (0) for θ in equation (esinθ2cos(4θ))cosθ ,

x=(esinθ2cos(4θ))cosθ=(esin

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