Polar graphs really important and tangents

[phospho]

Hi, I really need help with this as exam is tomorrow

The question is to find the points on the cardioid r=a(1+costheta) where the tangents are perpendicular to the initial line

here is the answer

http://gyazo.com/e8b4cbd36f0ef71d0cdf13be256d8618

Why is pi not included in the solution, while if I was finding parallel to the initial line then pi would be included.

please help

 

[tiny-tim]

hi phospho!

Why is pi not included in the solution, while if I was finding parallel to the initial line then pi would be included.

you're solving dx/dθ = 0

but you're using an x,y graph, so you really need to solve dx/dy = 0

ie dx/dθ / dy/dθ = 0

the solutions to this are the same as the solutions to dx/dθ = 0, except if dy/dθ = 0 (which it is for θ = π)