Question 712635
<img src="http://latex.codecogs.com/gif.latex?\sin\left(\frac{\theta}{2}\right) = -\sqrt{\frac{1-\cos(\theta)}{2}}" title="X" /> ... Half Angle Formula (for this given angle)



<img src="http://latex.codecogs.com/gif.latex?\sin\left(\frac{-150}{2}\right) = -\sqrt{\frac{1-\cos(-150)}{2}}" title="X" />



<img src="http://latex.codecogs.com/gif.latex?\sin\left(\frac{-150}{2}\right) = -\sqrt{\frac{1+\cos(150)}{2}}" title="X" />


<img src="http://latex.codecogs.com/gif.latex?\sin\left(\frac{-150}{2}\right) = -\sqrt{\frac{1+\frac{\sqrt{3}}{2}}{2}}" title="X" />


<img src="http://latex.codecogs.com/gif.latex?\sin\left(\frac{-150}{2}\right) = -\sqrt{\frac{1}{2}+\frac{\sqrt{3}}{4}}" title="X" />


<img src="http://latex.codecogs.com/gif.latex?\sin\left(\frac{-150}{2}\right) = -\sqrt{\frac{2}{4}+\frac{\sqrt{3}}{4}}" title="X" />


<img src="http://latex.codecogs.com/gif.latex?\sin\left(\frac{-150}{2}\right) = -\sqrt{\frac{2+\sqrt{3}}{4}}" title="X" />


<img src="http://latex.codecogs.com/gif.latex?\sin\left(\frac{-150}{2}\right) = -\frac{\sqrt{2+\sqrt{3}}}{\sqrt{4}}" title="X" />


<img src="http://latex.codecogs.com/gif.latex?\sin\left(\frac{-150}{2}\right) = -\frac{\sqrt{2+\sqrt{3}}}{2}" title="X" />


<img src="http://latex.codecogs.com/gif.latex?\sin\left(-75\right) = -\frac{\sqrt{2+\sqrt{3}}}{2}" title="X" />



Answer:  <img src="http://latex.codecogs.com/gif.latex?\sin\left(-75\right) = -\frac{\sqrt{2+\sqrt{3}}}{2}" title="X" />