What is the distance between #(2 ,(3 pi)/4 )# and #(2 , (11 pi )/8 )#?

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Answer 1 · 2016-10-21T09:28:51

The distance between given points is #3.326#.

The distance between two points given their polar coordinates #(r_1,theta_1)# and #(r_2,theta_2)# is given by

#sqrt(r_1^2+r_2^2-2r_1r_2cos(theta_1-theta_2))#

Hence, distance between #(2,(3pi)/4)# and #(2,(11pi)/8)# is

#sqrt(2^2+2^2-2xx2xx2xxcos((11pi)/8-(3pi)/4))#

= #sqrt(4+4-8cos((5pi)/8)#

= #sqrt(8xx(1-(-0.3827))#

= #sqrt(8xx1.3827)#

= #sqrt11.0616#

= #3.326#
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