Prove the formulae: \(\arcsin (- x) = - \arcsin x\), \(\arccos (- x) = \pi - \arccos x\).
In the centre of a rectangular billiard table that is 3 m long and 1 m wide, there is a billiard ball. It is hit by a cue in a random direction. After the impact the ball stops passing exactly 2 m. Find the expected number of reflections from the sides of the table.