Points $(6, 2)$ $(6 ,2 )$ and $(7, 5)$ $(7 ,5 )$ are $\frac{2 π}{3}$ $(2 pi)/3$ radians apart on a circle. What is the shortest arc length between the points?

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Answer 1 · 2018-02-04T05:38:16

Shortest arc length $s = R \cdot θ = 3.8239$ $s = R * theta = color(green)(3.8239$

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Given $θ = \frac{2 π}{3} = 120^{0}$ $theta = (2pi)/3 = 120^0$ #

$c = \sqrt{{(7 - 6)}^{2} + {(5 - 2)}^{2}} = 3.1623$ $c = sqrt((7-6)^2 + (5-2)^2) = 3.1623$

$r = \frac{c}{2 sin (\frac{2 π}{6})} = \frac{3.1623}{2 \cdot sin 60} = 1.8258$ $r = c / (2 sin ((2pi)/6)) = 3.1623 / (2 * sin 60) = 1.8258$

Shortest arc length $s = R \cdot θ = 1.8258 \cdot (\frac{2 π}{3}) = 3.8239$ $s = R * theta = 1.8258 * ((2pi) / 3) = color(green)3.8239$

Points (6,2)(6 ,2 ) and (7,5)(7 ,5 ) are 2π3(2 pi)/3 radians apart on a circle. What is the shortest arc length between the points?