Points $(2, 4)$ $(2 ,4 )$ and $(4, 9)$ $(4 ,9 )$ are $\frac{3 π}{4}$ $(3 pi)/4$ radians apart on a circle. What is the shortest arc length between the points?

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Points $(2, 4)$ $(2 ,4 )$ and $(4, 9)$ $(4 ,9 )$ are $\frac{3 π}{4}$ $(3 pi)/4$ radians apart on a circle. What is the shortest arc length between the points?

1 Answer

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Answer 1 · 2018-02-04T05:54:41

Shortest Arc length $s = r \cdot θ = 6.8669$ $s = r * theta = color(green)(6.8669$

Explanation:

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Chord $c = \sqrt{{(4 - 2)}^{2} + {(9 - 4)}^{2}} = 5.3852$ $c = sqrt((4-2)^2 + (9-4)^2) = 5.3852$

radius $r = \frac{c}{2 sin (\frac{θ}{2})} = \frac{5.3852}{2 \cdot sin (\frac{3 π}{8}) = 2.9144}$ $r = c / (2 sin (theta/2)) = 5.3852 / (2 * sin ((3pi)/8) = 2.9144$

Shortest Arc length $s = r \cdot θ = 2.9144 \cdot (\frac{3 π}{4}) = 6.8669$ $s = r * theta = 2.9144 * ((3pi)/4) = color(green)(6.8669$

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Points $(2, 4)$ $(2 ,4 )$ and $(4, 9)$ $(4 ,9 )$ are $\frac{3 π}{4}$ $(3 pi)/4$ radians apart on a circle. What is the shortest arc length between the points?

1 Answer

Explanation:

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Points (2 ,4 )(2,4)(2 ,4 ) and (4 ,9 )(4,9)(4 ,9 ) are (3 pi)/4 3π4(3 pi)/4 radians apart on a circle. What is the shortest arc length between the points?

1 Answer

Explanation:

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Points $(2, 4)$ $(2 ,4 )$ and $(4, 9)$ $(4 ,9 )$ are $\frac{3 π}{4}$ $(3 pi)/4$ radians apart on a circle. What is the shortest arc length between the points?