What is the distance between $(5 ,( pi)/4 )$ and $(3 , (11 pi )/12 )$ ?

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Answer 1 · 2016-05-25T20:48:51

The distance is $sqrt(19)$ .

I asume that your two points are in polar coordinates.
If so, we have the two points:

$r_1=5, theta_1=pi/4$
$r_2=3, theta_2=11/12pi$

the distance of two points in polar coordinates is given by

$d=sqrt(r_1^2+r_2^2-2r_1r_2cos(theta_1-theta_2))$

for you this is

$d=sqrt(5^2+3^2-2*3*5*cos(pi/4-11/12pi))$
$d=sqrt(25+9-30cos(-2/3pi))$
$d=sqrt(34-30cos(2/3pi))$
$d=sqrt(34-30*1/2)$
$d=sqrt(19)$

What is the distance between (5 ,( pi)/4 )(5 ,( pi)/4 ) and (3 , (11 pi )/12 )(3 , (11 pi )/12 )?