Use Symmetry to Graph Polar Equations
-$r = 2 \sin 3 \theta ;$ 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 $r = 2 \sin 3 \theta$ exhibits symmetry with respect to the line $\theta = \frac{\pi}{2}$ because sine functions are symmetric about $\theta = \frac{\pi}{2}$. This means that for any point on the graph, its reflection across the line $\theta = \frac{\pi}{2}$ will also be on the graph.

Use Symmetry to Graph Polar Equations - r=2sin⁡3θ;r = 2 \sin 3 \theta ;r=2sin3θ;

Use Symmetry to Graph Polar Equations
- $r = 2 \sin 3 \theta ;$