What is the distance between $(3 ,( pi)/4 )$ and $(-2 , ( pi )/2 )$ ?

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Answer 1 · 2017-02-05T09:37:11

$D=+-sqrt(13+6sqrt(2))$ or $D~~+-4.64$

You are given two points in polar coordinates

The distance formula for polar coordinates is

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

Plug in the values above

$D^2=3^2+(-2)^2-2(3)(-2)cos(pi"/"2-pi"/"4)$
$D^2=9+4+12cos(pi"/"4)$
$D^2=13+12(sqrt(2)/2)$
$D^2=13+6sqrt(2)$

Now take the square root of both sides

$D=+-sqrt(13+6sqrt(2))$
$D~~+-4.64$

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