What is the distance between the following polar coordinates?: $(3, \frac{π}{2}), (2, \frac{13 π}{12})$ $(3,(pi)/2), (2,(13pi)/12)$

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What is the distance between the following polar coordinates?: $(3, \frac{π}{2}), (2, \frac{13 π}{12})$ $(3,(pi)/2), (2,(13pi)/12)$

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Answer 1 · 2016-11-09T14:02:13

$∣ ∣ ∣ (3, \frac{π}{2}) : (2, \frac{13 π}{12}) ∣ ∣ ∣ = 4.9589$ $abs((3,pi/2):(2,(13pi)/12)) =4.9589$ (approx.)

Explanation:

Converting the polar coordinates to rectangular form:
(see image to help see the relationship)

$P t_{1} = (3, \frac{π}{2}) \to (3, 0)$ $color(red)(Pt_1 =(3,pi/2) rarr (3,0)$

$P t_{2} = (2, \frac{13 π}{12}) \to (- 2 cos (\frac{π}{12}), - 2 sin (\frac{π}{12})) \approx (- 1.93185, - 0.51764)$ $color(blue)(Pt_2=(2,(13pi)/12) rarr (-2cos(pi/12),-2sin(pi/12))~~(-1.93185,-0.51764))$

$| P t_{1} : P t_{2} | = \sqrt{{(3 - (- 1.93185))}^{2} + {(0 - (- 0.51764))}^{2}} \approx 4.9589$ $abs(Pt_1:Pt_2) = sqrt((3-(-1.93185))^2+(0-(-0.51764))^2)~~4.9589$

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What is the distance between the following polar coordinates?: $(3, \frac{π}{2}), (2, \frac{13 π}{12})$ $(3,(pi)/2), (2,(13pi)/12)$

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Explanation:

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What is the distance between the following polar coordinates?: (3,(pi)/2), (2,(13pi)/12) (3,π2),(2,13π12) (3,(pi)/2), (2,(13pi)/12)

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What is the distance between the following polar coordinates?: $(3, \frac{π}{2}), (2, \frac{13 π}{12})$ $(3,(pi)/2), (2,(13pi)/12)$