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)/3)# and #(r_2,theta_2)# represent #(1,(3pi)/4)#.
#implies d=sqrt(3^2+1^2-2*3*1Cos((-7pi)/3-(3pi)/4)#
#implies d=sqrt(9+1-6Cos((-28pi-9pi)/12)#
#implies d=sqrt(10-6Cos((-37pi)/12)#
#implies d=sqrt(10-6(-0.9659))#
#implies d=sqrt(10+5.7954)=sqrt(15.7954)=3.9743# units
#implies d=3.9743# units (approx)
Hence the distance between the given points is #3.9743# units.
