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

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