What is the distance between #(-5 ,( 5 pi)/12 )# and #(3 , ( pi )/2 )#?

1 Answer
A. S. Adikesavan
Feb 26, 2016

#sqrt# ( 34 + 30 sin 5#pi#/12 ). = 7.936 units, nearly.

Explanation:

The radial vectors to the points are #-#5 (cos 5#pi#/12, sin 5#pi#12 ) and 3 ( cos #pi#/2, sin #pi#/2 ) = ( 0, 3).
The vector joining these points is the difference ( 5 cos #pi#/12, 3 + 5 sin 5#pi#/12 ).
The length of this vector is the distance between the points.
It simplifies to #sqrt# ( 34 + 30 sin 5#pi#/12 ).
5#pi#/12 = 75 deg.

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