By considering the graph of y=sinx prove that, for 0 £ x £ p/2,

2x p £ sinx £ x.

By considering the graph of y=tanx prove that, for 0 < a < b < p/2,

tana tanb < a b .

You can use the excellent shareware Graphmatica (downloadable from http://nrich.maths.org/downloads/graphmatica.zip ), or a graphic calculator, to experiment with the graphs here.