Why is r=3cos2theta not symmetric over theta=pi/2?

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1 Answer
Jul 19, 2017

The graph IS symmetric about that line.

Explanation:

You already see the graph, so you were able to observe its symmetry.
One test to determine symmetry about theta = pi/2 is to substitute
theta - pi for theta.

3cos(2(theta -pi)) = 3cos(2theta -2pi)
=3cos2thetacos2pi+sin2thetasin2pi
=3cos2theta.

Therefore, the function is symmetric about theta = pi/2.