Test the equation for symmetry with respect to the given axis, line, or pole.
-$\mathrm { r } = - 4 \cos \theta$; the polar axis
A) May or may not be symmetric with respect to the polar axis
B) Symmetric with respect to the polar axis

Question

Quizplus · Accepted Answer

To test for symmetry with respect to the polar axis, replace $\theta$ with $-\theta$ in the equation. If the equation remains unchanged, it is symmetric with respect to the polar axis. Here, replacing $\theta$ with $-\theta$ gives $\mathrm { r } = - 4 \cos (-\theta)$, and since $\cos(-\theta) = \cos(\theta)$, the equation remains unchanged, indicating symmetry with respect to the polar axis.

Test the Equation for Symmetry with Respect to the Given r=−4cos⁡θ\mathrm { r } = - 4 \cos \thetar=−4cosθ

Test the Equation for Symmetry with Respect to the Given $\mathrm { r } = - 4 \cos \theta$