Question

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

Answer 1

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

Explanation:

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`