Lines of symmetry and Polar Coordinates

[ed2288]

Hi I'm trying to understand this technique for testing wether a polar curve is symmetrical about the line θ=α. I am told that if f(2α-θ) = f(θ) then θ=α is a line of symmetry. Can you help me to understand this!? An example would be great! thanks

[wickham]

Easily seen to be true if you sketch a simple diagram showing: the initial line; the line theta=alpha; the ray to (r, theta) and the ray to (r, 2alpha-theta). It is easy to see that the two rays are of equal length and are equally inclined at angle (alpha-theta) to the line theta=alpha. Therefore the line is a line of symmetry. Hope that helps, as I said, a diagram makes it obvious. Good luck.