Question Evaluate $\sin(-3\pi/8)$ using half-angle formula. Find measure of angle $\alpha$ where $\alpha/2=-3\pi/8$. Determine quadrant of half-angle $\alpha/2$.

Studdy Solution
Simplify the square root.
$$\sin\left(-\frac{3\pi}{8}\right) = -\sqrt{\frac{2 + \sqrt{2}}{4}} = -\frac{\sqrt{2 + \sqrt{2}}}{2}$$
The exact value of $\sin\left(-\frac{3\pi}{8}\right)$ is $-\frac{\sqrt{2 + \sqrt{2}}}{2}$.
b. The measure of angle $\alpha$ is given as $\alpha = -\frac{3\pi}{4}$.
c. The terminal side of the half-angle $\frac{\alpha}{2}$ lies in Quadrant III, as determined in steps 2 and 3.