What is the distance between the following polar coordinates?: # (7,(pi)/4), (8,(11pi)/8) #

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Answer 1 · 2017-09-29T06:21:58

Distance is #14.71#

Polar coordinates #(7,pi/4)# and #(8,(11pi)/8)# can be written in Cartesian coordinates as

#(7cos(pi/4),7sin(pi/4))# or #(7/sqrt2,7/sqrt2)#

i.e. #(4.95,4.95)# and

#(8cos((11pi)/8),8sin((11pi)/8))#

or #8xx(-0.3827),8xx(-0.9239))# or #(-3.0616,-7.3912)#

Hence, distance between them is

#sqrt((4.95+3.0616)^2+(4.95+7.3912)^2)#

= #sqrt(64.1857+152.3052)#

= #sqrt216.4909#

= #14.71#