Show that `f(x)=sinx` is increasing on `(0,\ pi//2)` and decreasing on `(pi//2,\ pi)` and neither increasing nor decreasing in `(0,\ pi)` .

Explanation

`f(x) = sin x`
` rArr f'(x) = cos x `
(a) `forall x in (0,pi/2), cos x gt 0`
`rArr f'(x) gt 0`
` rArr f(x) = sin x" is strictly increasing in "(0,pi/2)`
(b) ` forall x in (pi/2,pi), cos x lt 0`
` rArr f'(x) lt 0`
`rArr f(x) = sin x" is strictly decreasing in "(pi/2,pi)`
(c) `f(x) = sin x" is strictly increasing in " (0,pi/2)`
and strictly decreasing in `(pi/2,pi)`, so f(x) is neither increasing nor decreasing in `(0, pi)`.