Question

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

Answer 1

Shortest Arc length `s = r * theta = color(green)(6.8669`

Explanation:

Chord `c = sqrt((4-2)^2 + (9-4)^2) = 5.3852`

radius `r = c / (2 sin (theta/2)) = 5.3852 / (2 * sin ((3pi)/8) = 2.9144`

Shortest Arc length `s = r * theta = 2.9144 * ((3pi)/4) = color(green)(6.8669`