# Precal Proof for distance between 2 polar points

• November 21st 2008, 09:50 AM
rwc123
Precal Proof for distance between 2 polar points
Use the Law of Cosines to prove that the distance between 2 polar points (r1, θ1) and (r2, θ2) is d2=r12+r22-2r1r2cos(θ2-θ1)
• November 21st 2008, 10:08 AM
galactus
Let $P_{1}(r_{1},{\theta}_{1}) \;\ and \;\ P_{2}(r_{2}, {\theta}_{2})

$
be points in the $r{\theta}$ plane.

Let $a=r_{1}, \;\ b=r_{2}, \;\ c=d(P_{1},P_{2})$

and ${\gamma}={\theta}_{2}-{\theta}_{1}$

Sub these into the law of cosines, $c^{2}=a^{2}+b^{2}-2abcos{\gamma}$, gives the formula.