What is the distance between #(-3 , (17 pi)/12 )# and #(-1 , pi/4 )#?

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Answer 1 · 2016-07-15T00:39:38

The polar coordinates of two points.

#A->r_1=-3,theta_1=(17pi)/12#

#B->r_2=-1,theta_2=pi/4#

Then the distance between A,B

#d=sqrt(r_1^2+r_2^2+2r_1r_2cos(theta_1-theta_2))#

#d=sqrt((-3)^2+(-1)^2+2(-3)(-1)cos("17pi"/12-pi/4))#

#=>d=sqrt(9+1+6*cos("14pi"/12))#

#=>d=sqrt(9+1+6*cos("7pi"/6))#

#=>d=sqrt(9+1+6*cos(pi+pi/6))#

#=>d=sqrt(10-6*cos(pi/6))#

#=>d=sqrt(10-6*sqrt3/2)#

#=>d=sqrt(10-3sqrt3)#