In order to calculate the distance from two points in polar
coordinates, we use the polar coordinates distance formula. In
order to derive the polar coordinates distance formula, we use
the law of cosines. We can also use the polar coordinates
distance formula to help us come up with the polar equation for
a circle centered at the origin. I want to derive the distance
formula in polar coordinates and to do this I'm going to need to
recall the law of cosines. If you have a triangle, it's not
necessarily a right triangle and you know three, two sides and
the angle between them, you can find the third side using this
formula, c squared equals a squared plus b squared minus 2ab
cosine theta. And again a and b are the 2 known sides, theta's
the angle between them. Alright. Let's look at our picture here.
I've graphed 2 points in polar coordinates. One is r1 theta 1,
the other's r2 theta 2. I want to fi nd the distance between
these points. Now in order to do this I need the length of these
2 sides and I need this