Use Symmetry to Graph Polar Equations
-$r = 4 + 2 \sin \theta ;$ the line $\theta = \frac { \pi } { 2 }$
A) has symmetry with respect to the line $\theta = \frac { \pi } { 2 }$
B) may or may not have symmetry with respect to the line $\theta = \frac { \pi } { 2 }$

Question

Quizplus · Accepted Answer

The polar equation $r = 4 + 2 \sin \theta$ is symmetric with respect to the line $\theta = \frac{\pi}{2}$ because the sine function is symmetric about $\theta = \frac{\pi}{2}$. This means that for any value of $\theta$, the value of $r$ will be the same for $\theta$ and $\pi - \theta$, which corresponds to reflection across the line $\theta = \frac{\pi}{2}$.

Use Symmetry to Graph Polar Equations - r=4+2sin⁡θ;r = 4 + 2 \sin \theta ;r=4+2sinθ;

Use Symmetry to Graph Polar Equations
- $r = 4 + 2 \sin \theta ;$