Answer
$$-1$$
Work Step by Step
To evaluate trigonometric functions without a calculator, it is necessary to use the unit circle. Doing this, we find that the function evaluates to:
$$\tan \left(135^{\circ \:}\right) \\ \frac{\sin \left(135^{\circ \:}\right)}{\cos \left(135^{\circ \:}\right)} \\ \frac{\frac{\sqrt{2}}{2}}{\left(-\frac{\sqrt{2}}{2}\right)} \\ -1$$
