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

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Answer 1 · 2017-01-19T16:48:08

#sqrt(13+6sqrt(2+sqrt3))=4.959#, nearly.

Mark A (3, 5/12pi) and B (2, pi/2) that is same as B (2, -pi/2)#.

In the #triangle AOB, OA =3, OB = 2 and #

the anticlockwise #angle BOA=5/12pi-(-pi/12)=11/12pi#.

Now,

#AB=sqrt((OA)^2+(OB)^2-2(OA)(OB)cos angleBOA) #

#-sqrt(3^2+2^2-2(3)(2)cos(11/12pi))#

#=sqrt(13+12cospi/12))#

#=qrt(13+12sqrt(1/2(1+cos(pi/6))#

#=sqrt(13+6sqrt(2+sqrt3))=4.959#, nearly.