Question

Polar Coordinates: can someone explain the second formula? Why isn't it just: -r, 2n(pi) + theta?

Answer 1

http://tutorial.math.lamar.edu/Classes/CalcII/PolarCoordinates_files/eq0009MP.gif

Answer 2

http://tutorial.math.lamar.edu/Classes/CalcII/PolarCoordinates.aspx

Answer 3

the minus sign on the r changes the plot by rotating half the way around,

(r,θ)=(r,θ±2nπ)=(-r,θ±2nπ±π)=(-r,θ±(2n+1)π)