1. The problem asks to find the exact value of the trigonometric function for the angle $225^\circ$. 2. We recognize that $225^\circ$ is in the third quadrant where tangent is positive. 3. The reference angle for $225^\circ$ is $225^\circ - 180^\circ = 45^\circ$. 4. The tangent of $45^\circ$ is 1. 5. Since tangent is positive in the third quadrant, $\tan 225^\circ = 1$. Final answer: $$\tan 225^\circ = 1$$