Test the equation for symmetry with respect to the given axis, line, or pole.
-$\mathrm { r } ^ { 2 } = \sin ( 2 \theta )$; the pole
A) Symmetric with respect to the pole
B) May or may not be symmetric with respect to the pole

Question

Quizplus · Accepted Answer

To test for symmetry with respect to the pole, replace $\theta$ with $-\theta$. The equation becomes $r^2 = \sin(-2\theta)$, which simplifies to $r^2 = -\sin(2\theta)$ due to the odd property of sine. However, since $r^2$ must be non-negative, the original equation $r^2 = \sin(2\theta)$ is indeed symmetric with respect to the pole, as changing $\theta$ to $-\theta$ does not affect the set of points described by the equation in polar coordinates.

Test the Equation for Symmetry with Respect to the Given r2=sin⁡(2θ)\mathrm { r } ^ { 2 } = \sin ( 2 \theta )r2=sin(2θ)

Test the Equation for Symmetry with Respect to the Given $\mathrm { r } ^ { 2 } = \sin ( 2 \theta )$