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

1 Answer
A. S. Adikesavan
Mar 20, 2016

#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

Related questions
See all questions in Polar Coordinates
Impact of this question
1903 views around the world
You can reuse this answer
Creative Commons License