A particle moves on a straight line, with acceleration \(\ddot x \,cms^{-2}\) after \(t\) seconds given by \(\ddot x=\sin t-2 \sin 2t\). 

Initially the particle is at rest at the origin. Find

i) \(x\) as a function of \(t\)

ii) The velocity at \(t=\dfrac{\pi}{2}\) seconds