What is the distance between $(2 ,(7 pi)/6 )$ and $(2 , (23 pi )/12 )$ ?

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Answer 1 · 2018-02-19T08:51:14

Distance between the points $color(purple)(d = 1.5306$

Given : Polar coordinates $r_1 = (2, (7pi)/6), r_2 = (2,(23pi)/12)$

Formula for distance between two points, given the polar coordinates.

$d = sqrt ( r_1^2 + r_2 ^2 - 2 r_1 r_2 cos (theta_1 - theta_2))$

$d = sqrt((2^2 + 2^2 - (2 * 2 * 2 cos(((7pi)/6) - ((23pi)/12)))$

$=> sqrt(8 - 8cos((3pi)/4)) = 2 sqrt(2 - 2 cos (pi/4))$

$d = 2 sqrt(2 - sqrt2) = 2 sqrt(2 - 1.4142) = 2 sqrt(0.5858) ~~ color(purple)(1.5306$

What is the distance between (2 ,(7 pi)/6 )(2 ,(7 pi)/6 ) and (2 , (23 pi )/12 )(2 , (23 pi )/12 )?