Question

Determine if the graph is symmetric about the x-axis, the y-axis, or the origin.

r = -3 + 3 sin θ

y-axis only
Origin only
x-axis only
No symmetry

Answer 1

Think of the coordinate points \((r~,~\theta)\). \[(r,\theta) \rightarrow (-r,~\pi -\theta)
\implies \text{symmetric about x-axis}\]\[(r,\theta) \rightarrow (r,~\pi -\theta) \implies \text{symmetric about the y-axis} \]\[(r,\theta) \rightarrow (r,~ \theta +\pi ) \implies \text{symmetric about the origin}\] plugging in or analyzing coordinate points for these functions will usually tell you whether or not your function is symmetric, and about which axis or origin.