#(r,theta)# in polar coordinates is #(rcostheta,rsintheta)# in rectangular coordinates.
Hence, #(4,pi/12)# in rectangular coordinates is
#(4cos(pi/12),4sin(pi/12))# or
#(4xx0.9659,4xx0.2588)# or #(3.8636,1.0352)#
And, #(5,pi/12)# in rectangular coordinates is
#(5cos(pi/12),5sin(pi/12))# or
#(5xx0.9659,5xx0.2588)# or #(4.8295,1.294)#
The distance between the two points is #sqrt((4.8295-3.8636)^2+(1.294-1.0352)^2)# or #sqrt((0.9659)^2+(0.2588)^2)# or #sqrt(0.93296281+0.06697744)# or #sqrt(0.99994025)=1#
Actually the distance will be exactly #1# as both points have same #theta# coordinate, bur difference between #r# coordinate is exactly #1#. Minor difference has arisen because of rounding of numbers.
