Question4. Determine exact value for $2 \sin 112.5^{\circ} \cos 112.5^{\circ}$ : A. $\frac{1}{2}$ B. $-\frac{1}{2}$ C. $\frac{\sqrt{2}}{2}$ D. $-\frac{\sqrt{2}}{2}$

Studdy Solution
Find the exact value of $\sin(225^\circ)$. The angle $225^\circ$ is in the third quadrant, where sine is negative. It is equivalent to $180^\circ + 45^\circ$, so:
$$\sin(225^\circ) = -\sin(45^\circ)$$
We know that:
$$\sin(45^\circ) = \frac{\sqrt{2}}{2}$$
Therefore:
$$\sin(225^\circ) = -\frac{\sqrt{2}}{2}$$
The exact value for $2 \sin 112.5^\circ \cos 112.5^\circ$ is:
$$\boxed{-\frac{\sqrt{2}}{2}}$$