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 #(4,(5pi)/6)# and #(r_2,theta_2)# represent #(1,(-3pi)/2)#.
#implies d=sqrt(4^2+1^2-2*4*1Cos((5pi)/6-(-3pi)/2)#
#implies d=sqrt(16+1-8Cos((5pi)/6+(3pi)/2)#
#implies d=sqrt(17-8Cos((14pi)/6)#
#implies d=sqrt(17-8*0.5)=sqrt(17-4)=sqrt(13)=3.605# units
#implies d=3.605# units (approx)
Hence the distance between the given points is #3.605# units.
