Question

Points `(7 ,1 )` and `(5 ,9 )` are `(3 pi)/4` radians apart on a circle. What is the shortest arc length between the points?

Answer 1

`color(brown)("Length of shortest arc " (AB) = r * theta =10.5153`

Explanation:

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`"Point " A (7,1), " Point " B(5,9), hat (AOB) = theta = ((3pi) / 4)^c`

To find arc length S.

`"Chord Length " bar (AB) = sqrt ((7-5)^2 + (1-9)^2) = sqrt 68`

`hat (AOM) = hat (AOB) / 2 = (3pi)/8`

`bar(OA) = r = (AM) / sin (AOM) = (sqrt 68 / 2) / sin ((3pi)/8) = 4.4628`

`color(brown)("Length of shortest arc " (AB) = r * theta = 4.4628 * ((3pi)/4) = 10.5153`