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Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095

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Section
BuyFindarrow_forward

Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095
Textbook Problem

Sketching a Polar Graph In Exercises 87–96, sketch a graph of the polar equation.

r2 = 4 sin2 2 θ

To determine

To graph: The polar equation, r2=4sin22θ.

Explanation

Given:

The polar equation is r2=4sin22θ.

Graph:

Consider the equations,

r2=4sin22θ …… (1)

Rewrite the equation as,

r=±2sin(2θ)

The standard equation of rose petal curve is, r=asinnθ. The provided equation is like the rose petal curve equation.

So, the polar equation r2=4sin22θ is the equation of a Rose petal curve with four petals.

Now, construct the table for the values of r and θ after that plot them in the graph of polar plane.

For θ=0, substitute 0 for θ in equation (1);

r2=4sin22(0)=4(0)=0

For θ=π4, substitute π4 for θ in equation (1);

r2=4sin2[2(π4)]=4sin2(π2)=4(1)=4

So,

r=±4=±2

For θ=π2, substitute π2 for θ in equation (1);

r2=4sin2(2(π2))=4sin2(π)=4(0)=0

So,

r=±4=±2

For θ=π, substitute π for θ in equation (1);

r2=4sin2(2(π))=4sin2(2π)=4(0)=0

Continue the process up θ=2π

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