What is the distance between $(1 ,(3 pi)/4 )$ and $(3 , (15 pi )/8 )$ ?

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Answer 1 · 2016-03-10T12:34:58

Distance between $(1,(3pi)/4)$ and $(3,(15pi)/8)$ is $3.9425$

$(r,theta)$ in polar coordinates is $(rcostheta,rsintheta)$ in rectangular coordinates.

Hence, $(1,(3pi)/4)$ in rectangular coordinates is $(cos((3pi)/4),sin((3pi)/4))$ or $(-sqrt2/2,sqrt2/2)$ or $(-0.7071,0.7071)$

And $(3,(15pi)/8)$ in rectangular coordinates is $(3cos((15pi)/8),3sin((15pi)/8))$ or $(2.7716,-1.1481)$

Hence distance between $(-0.7071,0.7071)$ and $(2.7716,-1.1481)$ is

$sqrt((2.7716+0.7071)^2+(-1.1481-0.7071)^2)$ or
$sqrt((3.4787)^2+(-1.8552)^2)$ or
$sqrt(12.1014+3.4418)=sqrt(15.5432)=3.9425$

What is the distance between (1 ,(3 pi)/4 )(1 ,(3 pi)/4 ) and (3 , (15 pi )/8 )(3 , (15 pi )/8 )?