Question

Sin(-5пи/6)+ sin(пи/6)+sinпи+sin(-пи/4)

Answer 1

$sin(-\frac{5\pi}{6})+sin\frac{\pi}{6}+sin\pi +sin(-\frac{\pi}{4})=-sin(\pi -\frac{\pi}{6})+\frac{1}{2}+0-sin\frac{\pi}{4}=\\\\=-sin\frac{\pi}{6}+\frac{1}{2}-\frac{\sqrt2}{2}=-\frac{1}{2}+\frac{1}{2}-\frac{\sqrt2}{2}=-\frac{\sqrt2}{2}$