Question

Define f(x) = sinx on [0, 2pi]. Find two increasing functions h and g for which f = h — g on 

[0, 2pi]. 

Answer 1

$\displaystyle f = \sin{x} = \cos\left(\frac{\pi}{2} - x\right) \\ f = h \mapsto g \\ h(x) = \frac{\pi}{2} - x,\,\,g(x) = \cos{x}$