1. **State the problem:** Find the value of $\sin 135^\circ$. 2. **Recall the formula and rules:** The sine of an angle in degrees can be found using the unit circle or sine addition formulas. Note that $135^\circ = 180^\circ - 45^\circ$. 3. **Use the sine subtraction identity:** $$\sin(180^\circ - \theta) = \sin \theta$$ This means: $$\sin 135^\circ = \sin(180^\circ - 45^\circ) = \sin 45^\circ$$ 4. **Evaluate $\sin 45^\circ$:** $$\sin 45^\circ = \frac{\sqrt{2}}{2}$$ 5. **Final answer:** $$\sin 135^\circ = \frac{\sqrt{2}}{2}$$ This means the sine of 135 degrees is $\frac{\sqrt{2}}{2}$, which is positive because 135 degrees lies in the second quadrant where sine values are positive.