The distance formula for polar coordinates is
#d=sqrt(r_1^2+r_2^2-2r_1r_2Cos(theta_1-theta_2)#
Where #d# is the distance between the two points, #r_1#, and #theta_1# are the polar coordinates of one point and #r_2# and #theta_2# are the polar coordinates of another point.
Let #(r_1,theta_1)# represent #(3,(-7pi)/12)# and #(r_2,theta_2)# represent #(7,(5pi)/8)#.
#implies d=sqrt(3^2+7^2-2*3*7Cos((-7pi)/12-(5pi)/8)#
#implies d=sqrt(9+49-42Cos((-14pi-15pi)/24)#
#implies d=sqrt(58-42Cos((-29pi)/24))=sqrt(58-42*(-0.7933))=sqrt(58+33.3186)=sqrt(91.3186)=9.556# units
#implies d=9.556# units (approx)
Hence the distance between the given points is #9.556# units.
