#### Answer

$\lim\limits_{x \to \frac{\pi}{4}}\sin^{2}x = \frac{1}{2} = 0.5$

#### Work Step by Step

$\lim\limits_{x \to \frac{\pi}{4}}\sin{x}= \sin{\frac{\pi}{4}} = \frac{1}{\sqrt 2} = 0.707$
So,
$\lim\limits_{x \to \frac{\pi}{4}}\sin^{2}{x} = (\frac{1}{\sqrt 2})^{2} = \frac{1}{2} = 0.5$