Show that f(x)= is an increasing function on (- 2 , 2 ). - Vidyadip

Question

Show that $\text{f}(\text{x})=\sin\text{x}$ is an increasing function on $\Big(\frac{-\pi}{2},\frac{\pi}{2}\Big).$

✓

Answer

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

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