What is the distance between $(2, \frac{7 π}{6})$ $(2 ,(7 pi)/6 )$ and $(2, \frac{23 π}{12})$ $(2 , (23 pi )/12 )$ ?

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What is the distance between $(2, \frac{7 π}{6})$ $(2 ,(7 pi)/6 )$ and $(2, \frac{23 π}{12})$ $(2 , (23 pi )/12 )$ ?

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Answer 1 · 2018-02-19T08:51:14

Distance between the points $d = 1.5306$ $color(purple)(d = 1.5306$

Explanation:

Given : Polar coordinates $r_{1} = (2, \frac{7 π}{6}), r_{2} = (2, \frac{23 π}{12})$ $r_1 = (2, (7pi)/6), r_2 = (2,(23pi)/12)$

Formula for distance between two points, given the polar coordinates.

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

$d = \sqrt{(2^{2} + 2^{2} - (2 \cdot 2 \cdot 2 cos ((\frac{7 π}{6}) - (\frac{23 π}{12})))}$ $d = sqrt((2^2 + 2^2 - (2 * 2 * 2 cos(((7pi)/6) - ((23pi)/12)))$

$\Rightarrow \sqrt{8 - 8 cos (\frac{3 π}{4})} = 2 \sqrt{2 - 2 cos (\frac{π}{4})}$ $=> sqrt(8 - 8cos((3pi)/4)) = 2 sqrt(2 - 2 cos (pi/4))$

$d = 2 \sqrt{2 - \sqrt{2}} = 2 \sqrt{2 - 1.4142} = 2 \sqrt{0.5858} \approx 1.5306$ $d = 2 sqrt(2 - sqrt2) = 2 sqrt(2 - 1.4142) = 2 sqrt(0.5858) ~~ color(purple)(1.5306$

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What is the distance between $(2, \frac{7 π}{6})$ $(2 ,(7 pi)/6 )$ and $(2, \frac{23 π}{12})$ $(2 , (23 pi )/12 )$ ?

1 Answer

Explanation:

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What is the distance between (2,7π6)(2 ,(7 pi)/6 ) and (2,23π12)(2 , (23 pi )/12 )?

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What is the distance between $(2, \frac{7 π}{6})$ $(2 ,(7 pi)/6 )$ and $(2, \frac{23 π}{12})$ $(2 , (23 pi )/12 )$ ?