$[$Optimisation$]$ The pressure $P$ behind an airfoil over time fulfils the equation

$P=6cost-1\mathrm{.}5sint$

$($a$)$ Sketch the graph of $P(t),$ showing how the pressure changes with time. $(5$ marks$)$

$($b$)$ Apply three iterations of the Golden Section Search to determine the time $t$ at which the pressure $P$ is minimal. Use starting guesses $t_L=2s$ and $t_U=4s.$

Hint: Make sure your calculator is in radians.

$[2\mathrm{.}94$ s$](25$ marks$)$