### Instruction: Compute $\tan 135^\circ$.### Response: To find the tangent of an angle, I need to recall the definition of the tangent function in terms of sine and cosine.
I know that $\tan \theta = \frac{\sin \theta}{\cos \theta}$ for any angle $\theta$.
So, to find $\tan 135^\circ$, I just need to plug in $\theta = 135^\circ$ and simplify.
I also know that $\sin 135^\circ = \frac{\sqrt{2}}{2}$ and $\cos 135^\circ = -\frac{\sqrt{2}}{2}$ by using the unit circle and the reference angles.
So, I have $\tan 135^\circ = \frac{\sin 135^\circ}{\cos 135^\circ} = \frac{\frac{\sqrt{2}}{2}}{-\frac{\sqrt{2}}{2}} = -1$.