Determine the symmetries of the curve.
-$$r ^ { 2 } = 6 \cos 4 \theta$$
A) x-axis only
B) Origin only
C) y-axis only
D) x-axis, y-axis, origin

Question

Quizplus · Accepted Answer

The curve has both radial and reflectional symmetry about the origin. 
Radial symmetry can be seen by observing that $	heta$ and $-	heta$ result in the same $r$, and therefore the same point on the graph. Thus, the curve is symmetric about the origin.
Reflectional symmetry can be seen by observing that $r$ and $-r$ result in the same point on the graph, and so the curve is symmetric about both the x- and y-axes. Thus, the curve has x-axis, y-axis, and origin symmetry.

Determine the Symmetries of the Curve r2=6cos⁡4θr ^ { 2 } = 6 \cos 4 \thetar2=6cos4θ

Determine the Symmetries of the Curve $r ^ { 2 } = 6 \cos 4 \theta$