\(\displaystyle sin(150) = sin(30) = 1/2\)
\(\displaystyle cos(150) = -cos(30) = -\frac{sqrt{3}}{2}\\)
Use the half-angle formula:
\(\displaystyle \L\ sin^2(a) = \frac{1}{2}\(1 - cos(2a))\)
Put a = 75, so:
\(\displaystyle \L\ sin^2(75) = \frac{1}{2}\(1 + \frac{sqrt{3}}{2}\)\)
\(\displaystyle \L\ 4sin^2(75) = (2 + sqrt{3})\)
Solve for \(\displaystyle sin(75)\), but remember that it is in the 1st quadrant.
