Show that the function given by f(x) = sin x is (a) strictly increasing in (π/2, π) (b) strictly decreasing in (0,π/2)

Question

Show that the function given by f(x) = sin x is

(a) strictly increasing in (0,π/2)

(b) strictly decreasing in (π/2,π )

(c) neither increasing nor decreasing in (0,π )

Answer 1

The given function is f(x) = sin x.

(c) From the results obtained in (a) and (b), it is clear that f is neither increasing nor decreasing in (0, π).