What is the distance between $(- 3, \frac{5 π}{6})$ $(-3 ,(5 pi)/6 )$ and $(5, \frac{11 π}{12})$ $(5 , (11 pi )/12 )$ ?

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What is the distance between $(- 3, \frac{5 π}{6})$ $(-3 ,(5 pi)/6 )$ and $(5, \frac{11 π}{12})$ $(5 , (11 pi )/12 )$ ?

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Answer 1 · 2017-05-31T08:19:24

$\approx 7.936 to 3 dec. places$ $~~7.936" to 3 dec. places"$

Explanation:

$the distance ( d ) between 2 polar coordinates$ $"the distance ( d ) between 2 "color(blue)"polar coordinates"$ is.

$color(red)(bar(ul(|color(white)(2/2)color(black)(d^2=r_1^2+r_2^2-2r_1r_2cos(theta_2-theta_1))color(white)(2/2)|)))$

$"where " (r_1.theta_1),(r_2,theta_2)" are 2 points"$

$"the points are "$

$(r_1,theta_1)=(-3,(5pi)/6),(r_2,theta_2)=(5,(11pi)/12)$

$rArrd^2=(-3)^2+5^2-(2xx-3xx5cos((11pi)/12-(5pi)/6))$

$=9+25+30cos(pi/12)$

$~~62.9777..$

$rArrd=sqrt(62.9777..)~~7.936" to 3 decimal places"$

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What is the distance between $(- 3, \frac{5 π}{6})$ $(-3 ,(5 pi)/6 )$ and $(5, \frac{11 π}{12})$ $(5 , (11 pi )/12 )$ ?

1 Answer

Explanation:

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What is the distance between (-3 ,(5 pi)/6 )(−3,5π6)(-3 ,(5 pi)/6 ) and (5 , (11 pi )/12 )(5,11π12)(5 , (11 pi )/12 )?

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Explanation:

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What is the distance between $(- 3, \frac{5 π}{6})$ $(-3 ,(5 pi)/6 )$ and $(5, \frac{11 π}{12})$ $(5 , (11 pi )/12 )$ ?