What is the distance between the following polar coordinates?: # (5,(3pi)/4), (1,(9pi)/8) #

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Answer 1 · 2017-12-22T16:37:34

Distance between the polar coordinates is #4.71#

The polar coordinates #(5,(3pi)/4)# and #(1,(9pi)/8)#

in rectangular coordinates are

#(5cos((3p)/4),5sin((3p)/4)# i.e. #(-5/sqrt2,5/sqrt2)# or #(-3.5355,3.5355)#

and #(cos((9p)/8),sin((9p)/8))# i.e. #(-0.9239,-0.3827)#

Hence distance between two is

#sqrt((-3.5355+0.9239)^2+(3.5355+0.3827)^2)#

= #sqrt(2.6116^2+3.9182^2)#

= #sqrt(6.82045456+15.35229124)#

= #sqrt22.1727458#

= #4.71#