Points $(2, 6)$ $(2 ,6 )$ and $(5, 3)$ $(5 ,3 )$ 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 $(5, 3)$ $(5 ,3 )$ 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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Answer 1 · 2016-02-27T18:14:17

I have taken you up to the final calculation point

Explanation:

Tony B

$Determine the length AC$ $color(blue)("Determine the length AC")$

$A C = \sqrt{{(x_{1} - x_{2})}_{1}^{2} + {(y_{2} - y_{1})}_{2}^{2}} = \sqrt{18} = 3 \sqrt{2}$ $AC=sqrt( (x_1-x_2)^2+(y_2-y_1)^2) = sqrt(18)=3sqrt(2)$

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$Determine the length AB$ $color(blue)("Determine the length AB")$

$∠ C A B = \frac{π}{2} - \frac{∠ A B C}{2} = \frac{π}{2} - \frac{3 π}{8} = \frac{π}{8} \to (22 \frac{1}{2^{o}})$ $/_ CAB = pi/2-(/_ABC)/2 = pi/2-(3pi)/8 = pi/8 ->(22 1/2 ^o)$

$A B cos (\frac{π}{8}) = \frac{3 \sqrt{2}}{2}$ $ABcos(pi/8)= (3sqrt(2))/2$

$A B = \frac{3 \sqrt{2}}{2 cos (\frac{π}{8})}$ $AB=(3sqrt(2))/(2cos(pi/8))$
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$To determine arc length$ $color(blue)("To determine arc length")$

This is radius times radian count

$A B \times \frac{3 π}{4} = \frac{3 \sqrt{2}}{2 cos (\frac{π}{8})} \times \frac{3 π}{4}$ $ABxx (3pi)/4 =(3sqrt(2))/(2cos(pi/8)) xx(3pi)/4$

I will let you finish the calculation

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