Question

What is the distance between `(-6 , (-5 pi)/8 )` and `(1 , pi )`?

Answer 1

`sqrt(37-12 cos(5pi/8))` = 6.45, nearly

Explanation:

`(-r, theta) = (r, theta+pi)`.

So, keeping the sense of rotation for `theta` as anticlockwise, the `angle` between the radii to these points `A (6. 3pi/8) and B (1, pi)` from the origin O is `(pi-3pi/8)=5pi/8`.

From the `triangle`OAB, AB =`sqrt(OA^2+OB^2-2 .OA. OB cos (angle AOB)`.
OA = 6, OB =1 and `angle AOB = 5pi/8`.,

Also, you can convert to cartesian coordinates and find the distance