Question

Show that f(x) = sin x is an increasing function on (−π/2, π/2).

Answer 1

$$\begin{gathered} f\left(x\right)=\sin x \\ f\text{'}\left(x\right)=\cos x>0\forall x\in \left(\frac{-\mathrm{\pi }}{2},\frac{\mathrm{\pi }}{2}\right)\left[\because \mathrm{Cos}\mathrm{function}\mathrm{is}\mathrm{positive}\mathrm{in}\mathrm{first}\mathrm{and}\mathrm{fourth}\mathrm{quadrant}\right] \\ \text{So,}f\left(x\right)\text{is increasing on}\left(\frac{-\mathrm{\pi }}{2},\frac{\mathrm{\pi }}{2}\right)\text{.} \end{gathered}$$