What is the distance between the following polar coordinates?: $(2, \frac{π}{4}), (5, \frac{5 π}{8})$ $(2,(pi)/4), (5,(5pi)/8)$

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What is the distance between the following polar coordinates?: $(2, \frac{π}{4}), (5, \frac{5 π}{8})$ $(2,(pi)/4), (5,(5pi)/8)$

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Answer 1 · 2017-04-16T13:03:28

$4.6$ $4.6$ to 2dp

Explanation:

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If we denote $(2, \frac{π}{4})$ $(2,pi/4)$ by $A$ $A$ , $(5, \frac{5 π}{8})$ $(5,(5pi)/8)$ by $B$ $B$ and the origin by $O$ $O$ , and the angle $∠ A O B$ $angle AOB$ by $θ$ $theta$ , Then:

$θ = \frac{5 π}{8} - \frac{π}{4} = \frac{3 π}{8}$ $theta = (5pi)/8- pi/4 = (3pi)/8$

If we apply the cosine rule:

$a^{2} = b^{2} + c^{2} - 2 a b cos A$ $a^2 = b^2 + c^2 - 2abcosA$

Then we get:

${(A B)}^{2} = {(O A)}^{2} + {(O B)}^{2} - 2 (O A) (O B) cos θ$ $(AB)^2 = (OA)^2 + (OB)^2 - 2(OA)(OB)costheta$
$= {(2)}^{2} + {(5)}^{2} - 2 (2) (5) cos (\frac{3 π}{8})$ $" " = (2)^2 + (5)^2 - 2(2)(5)cos((3pi)/8)$
$= 4 + 25 - 20 cos (\frac{3 π}{8})$ $" " = 4+25 - 20cos((3pi)/8)$
$= 29 - 20 cos (\frac{3 π}{8})$ $" " = 29 - 20cos((3pi)/8)$
$" " = 21.34633...$

$:. AB = 4.629209$

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What is the distance between the following polar coordinates?: $(2, \frac{π}{4}), (5, \frac{5 π}{8})$ $(2,(pi)/4), (5,(5pi)/8)$

1 Answer

Explanation:

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What is the distance between the following polar coordinates?: (2,(pi)/4), (5,(5pi)/8) (2,π4),(5,5π8) (2,(pi)/4), (5,(5pi)/8)

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What is the distance between the following polar coordinates?: $(2, \frac{π}{4}), (5, \frac{5 π}{8})$ $(2,(pi)/4), (5,(5pi)/8)$