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