What is the distance between $(5, \frac{π}{4})$ $(5 ,( pi)/4 )$ and $(3, \frac{11 π}{12})$ $(3 , (11 pi )/12 )$ ?

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What is the distance between $(5, \frac{π}{4})$ $(5 ,( pi)/4 )$ and $(3, \frac{11 π}{12})$ $(3 , (11 pi )/12 )$ ?

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Answer 1 · 2016-05-25T20:48:51

The distance is $\sqrt{19}$ $sqrt(19)$ .

Explanation:

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

$r_{1} = 5, θ_{1} = \frac{π}{4}$ $r_1=5, theta_1=pi/4$
$r_{2} = 3, θ_{2} = \frac{11}{12} π$ $r_2=3, theta_2=11/12pi$

the distance of two points in polar coordinates is given by

$d = \sqrt{r_{1}^{2} + r_{2}^{2} - 2 r_{1} r_{2} cos (θ_{1} - θ_{2})}$ $d=sqrt(r_1^2+r_2^2-2r_1r_2cos(theta_1-theta_2))$

for you this is

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

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What is the distance between $(5, \frac{π}{4})$ $(5 ,( pi)/4 )$ and $(3, \frac{11 π}{12})$ $(3 , (11 pi )/12 )$ ?

1 Answer

Explanation:

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What is the distance between (5 ,( pi)/4 )(5,π4)(5 ,( pi)/4 ) and (3 , (11 pi )/12 )(3,11π12)(3 , (11 pi )/12 )?

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Explanation:

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What is the distance between $(5, \frac{π}{4})$ $(5 ,( pi)/4 )$ and $(3, \frac{11 π}{12})$ $(3 , (11 pi )/12 )$ ?