We can use the angle addition formula for sine to write $\sin 150^\circ$ as $\sin(90^\circ+60^\circ)$.
Using the angle addition formula, we have $\sin(90^\circ+60^\circ)=\sin 90^\circ \cos 60^\circ + \cos 90^\circ \sin 60^\circ$.
Since $\sin 90^\circ=1$ and $\cos 90^\circ=0$, we can simplify to $\sin 150^\circ = 1\cdot \frac{1}{2} + 0\cdot \frac{\sqrt{3}}{2} = \boxed{\frac{1}{2}}$.
The answer is: \frac{1}{2}
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
Compute $\sin 150^\circ$.

### Answer:
