Distance between Two Points in Plane in Polar Coordinates

Theorem
Let $A = \polar {r_1, \theta_1}$ and $B = \polar {r_2, \theta_2}$ be two points in a polar coordinate plane

The distance $d$ between $A$ and $B$ is given by:
 * $d = \sqrt {r_1^2 + r_2^2 + 2 r_1 r_2 \map \cos {\theta_1 - \theta_2} }$

Also presented as
This result can also be seen presented as:


 * $d = \sqrt {r_1^2 + r_2^2 + 2 r_1 r_2 \map \cos {\theta_2 - \theta_1} }$

The equivalence of the results follows from the fact that $\map \cos {\theta_2 - \theta_1} = \map \cos {\theta_1 - \theta_2}$.

Also see

 * Distance Formula


 * Complex Modulus of Difference of Complex Numbers