Horse Grazing

Calculus Level 4

A horse is tethered by a rope fastened at one end \(A\) on the boundary of a circular field whoose center is \(O\). The horse can graze over \(\dfrac { 1 } { 7 }\) the part of the field reaching the farthest point \(B\) on the boundary that he can reach. If \(\angle AOB = \theta \). Find the value of \[\dfrac { 7(\sin { \theta +\left( \pi -\theta \right) \cos { \theta } ) } }{ \pi }. \]

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