During the spin cycle the time dependent angular speed of a washing machine drum is given by the equation $($t$)=$ at $+$ bt$2-$ ct$4$ where a $=2\mathrm{.}6$ rad$/$s$2,$ b $=0\mathrm{.}65$ rad$/$s$3$ and c $=0\mathrm{.}045$ rad$/$s$5.$ At time t $=0$ s$,$ a point P on the washer drum is located at $0=0\mathrm{.}65$ rad.Write an equation for the angular position of the point P$,$ as a function of time, in terms of the given parameters.

$($t$)$