Points #(2 ,2 )# and #(8 ,1 )# are #(5 pi)/3 # radians apart on a circle. What is the shortest arc length between the points?

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Answer 1 · 2018-01-10T09:45:28

Shortest arc length #S = color (blue)(6.3699)#

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W.r.t. the figure,

#C = sqrt((8-2)^2 + (1-2)^2) = sqrt(37) = 6.0828#

#R = C / (2sin (theta/2)) = 6.0828 / (2 * sin((5pi)/6)) = 6.0828#

To find the Shortest arc length, center angle will be

#2pi - theta = 2pi - (5pi)/3 = pi / 3#

#S = R * theta =( 6.0828 * pi ) / 3 = 6.3699#