A particle \(P\) moves along an arc of a circle with centre \(O\) and radius 2 m . At time \(t\) seconds, the angle POA is \(\theta\), where \(\theta=1-\cos 2 t\), and \(A\) is a fixed point on the arc of the circle.
(i) Show that the magnitude of the radial component of the acceleration of \(P\) when \(t=\frac{1}{6} \pi\) is \(6 \mathrm{~m} \mathrm{~s}^{-2}\).
(ii) Find the magnitude of the transverse component of the acceleration of \(P\) when \(t=\frac{1}{6} \pi\).