What is the distance between the following polar coordinates?: $(5,(-5pi)/12), (5,(11pi)/6)$

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Answer 1 · 2017-06-18T08:38:37

$D=sqrt(50+50sqrt(2)/2)~~9.2388$

We are given

$r_1=5$
$theta_1=-(5pi)/12$

$r_2=5$
$theta_2=(11pi)/6$

The distance formula for polar coordinates is

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

$D=sqrt(5^2+5^2-2(5)(5)cos(-(5pi)/12-(11pi)/6))$

$D=sqrt(25+25-50cos(-(9pi)/4))$

$D=sqrt(50+50sqrt(2)/2)~~9.2388$

What is the distance between the following polar coordinates?: (5,(-5pi)/12), (5,(11pi)/6) (5,(-5pi)/12), (5,(11pi)/6)