Polar graph analysis:

  • graph (online/calculator ok)
  • find max $|r|$ value and all $\theta$ where it occurs
  • symmetry tests
    • x-axis, y-axis, origin (rotation by $\pi$)
    • look at graph and verify any symmetries you see (this example has all three, but you only need to check the ones you see on the graph)

Reference: OSP 8.4

example (pdf)