What is the distance between the following polar coordinates?: # (16,(19pi)/12), (11,(17pi)/8) #

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Answer 1 · 2016-05-09T12:15:09

Distance between the polar coordinates is #20.566#

A polar coordinate #(r,theta)# is #(rcostheta,rsintheta)# in Caresian coordinates.

Hence #(16,(19pi)/12)# is #(16cos(19pi)/12,16sin(19pi)/12)# or #(16xx0.2588,16xx-0.9659)# or #(4.1408,-15.4544)#

#(11,(17pi)/8)# is #(11cos(17pi)/8,11sin(7pi)/8)# or #(11xx0.9239,11xx0.3827)# or #(10.1629,4.2097)#

Hence distance between two points is given by #sqrt((10.1629-4.1408)^2+(4.2097+15.4544)^2)# or

#sqrt(6.0221^2+19.6641^2)#

= #sqrt(36.2657+386.6768)#

= #sqrt422.9425=20.566#