Answer
$\left( 6,\frac{5\pi }{3} \right)$
Work Step by Step
It is given that the horse is in the inner circle; therefore,
$r=6$
As the horse is $\frac{5}{6}$ of the way around the merry-go-round, therefore, the angle intercepted by the horse will be given by,
$2\pi \times \frac{5}{6}=\frac{5\pi }{3}$
Therefore, the polar coordinate is $\left( 6,\frac{5\pi }{3} \right)$.
