Points $(2, 6)$ $(2 ,6 )$ and $(5, 9)$ $(5 ,9 )$ 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 $(2, 6)$ $(2 ,6 )$ and $(5, 9)$ $(5 ,9 )$ 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 · 2018-01-10T10:08:53

Shortest arc length $S = r \cdot θ \approx 5.41$ $S = r * theta ~~color(red)(5.41)$

Explanation:

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$C = (\frac{3 π}{4})$ $C = ((3pi)/4)$

Chord $C h = \sqrt{{(5 - 2)}^{2} + {(9 - 6)}^{2}} = 4.2426$ $Ch = sqrt((5-2)^2 + (9-6)^2) = 4.2426$

Using Pythagoras theorem,

$r = C \frac{h}{2 \cdot sin (\frac{C}{2})} = \frac{4.2426}{2 \cdot sin (\frac{3 π}{8}) = 2.2961}$ $r = Ch / (2* sin (C/2)) = 4.2426 / (2 * sin ((3pi)/8) = 2.2961$

Shortest arc length $S = r \cdot C = 2.2961 \cdot (\frac{3 π}{4}) \approx 5.41$ $S = r * C = 2.2961 * ((3pi)/4) ~~color(red)(5.41)$

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Points $(2, 6)$ $(2 ,6 )$ and $(5, 9)$ $(5 ,9 )$ 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 ,6 )(2,6)(2 ,6 ) and (5 ,9 )(5,9)(5 ,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 $(2, 6)$ $(2 ,6 )$ and $(5, 9)$ $(5 ,9 )$ are $\frac{3 π}{4}$ $(3 pi)/4$ radians apart on a circle. What is the shortest arc length between the points?