   Chapter 10, Problem 5RQ

Chapter
Section
Textbook Problem

Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.5. The polar curves r = 1 − sin 2 θ r = sin 2 θ − 1 have the same graph.

To determine

To find: Whether the given statement is true or false and explain with an example if necessary to prove your answer.

Explanation

Given:

The polar equation of the variable r is as follows.

r=1sin2θ (1)

The parametric equation of the variable y is as follows.

r=sin2θ1 (2)

Calculation:

Rotate the equation (1) by 180° about the O.

r=1sin2(θ+π)=1sin(2θ+2π)=1sin

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