The given problem is asking for the value of $\cos 225^\circ$, and it states that the value is $-\frac{\sqrt{2}}{2}$.

Let’s verify this:

1. The angle $225^\circ$ lies in the third quadrant of the unit circle.
2. In the third quadrant, the cosine of any angle is negative.
3. The reference angle for $225^\circ$ is $225^\circ - 180^\circ = 45^\circ$.
4. The cosine of $45^\circ$ is $\frac{\sqrt{2}}{2}$.
5. Since $225^\circ$ is in the third quadrant, the cosine value becomes $-\frac{\sqrt{2}}{2}$.

Thus, the given value $-\frac{\sqrt{2}}{2}$ is correct for $\cos 225^\circ$.

Do you have any additional questions or need further clarifications? Here are 5 questions that may help expand your understanding:

1. What is the sine value of $225^\circ$?
2. How do you find the reference angle for any given angle?
3. What is the general rule for the sign of cosine in each quadrant?
4. Can you verify the same result for $225^\circ$ using radians instead of degrees?
5. How is the cosine value for $225^\circ$ derived from the unit circle?

Tip: Always determine the quadrant of an angle to correctly apply the sign for trigonometric values.