What is the distance between the following polar coordinates?: # (6,(7pi)/12), (2,(-3pi)/8) #

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Answer 1 · 2016-03-15T07:51:53

#d = 2sqrt(10 - 3sqrt( 2 + sqrt ( 2 - sqrt 3 ) )#

#d = sqrt(r_1^2+r_2^2 - 2r_1r_2cos(phi_2-phi_1))#

#d = sqrt(6^2+2^2 - 2*6*2*cos(-(3pi)/8-(7pi)/12)#

#d = sqrt(40 - 24*cos((-29pi)/24)#

#d = 2sqrt(10 - 6cos((29pi)/24)#

#cos((29pi)/6) = cos(4pi + (5pi)/6) = cos((5pi)/6) = -sqrt3/2#

#cos((29pi)/12) = cos(((29pi)/6)/2) = sqrt((1+cos((29pi)/6))/2)#

#cos((29pi)/12) = sqrt((1-sqrt3/2)/2) = sqrt((2-sqrt3)/4) = sqrt(2-sqrt3) /2 #

#cos((29pi)/24) = cos(((29pi)/12)/2) = sqrt((1+cos((29pi)/12))/2)#

#cos((29pi)/24) = sqrt( ( 1+ sqrt( ( 2-sqrt3 ) ) / 2 ) /2 ) #

#cos((29pi)/24) = sqrt( 2 + sqrt ( 2 - sqrt 3 ) ) /2#

#d = 2sqrt(10 - 6* sqrt( 2 + sqrt ( 2 - sqrt 3 ) ) /2)#

#d = 2sqrt(10 - 3sqrt( 2 + sqrt ( 2 - sqrt 3 ) )#