The unit circle is a circle with its center at $O=(0,0)$ and a radius of 1. If you have a point $A$ on the unit circle and an angle $\alpha$ spanning from the $x$-axis to the line $OA$, then the $x$-coordinate of the point $A$ is $\cos \alpha$ and the $y$-coordinate of the point $A$ is $\sin \alpha$.

This table shows the most essential angles in radians and in degrees. It is very useful to learn which radians correspond to these angles. You are expected to know the exact values for the sine, cosine and tangent of each of these.

By the use of trigonometric identities we can expand the table to many more angles.

For instance, you know that $\sin \frac{\pi }{4}=\frac{\sqrt{2}}{2}$ and that $\cos \frac{\pi }{4}=\frac{\sqrt{2}}{2}$, so then:

$$\tan \frac{\pi }{4}=\genfrac{}{}{1.0pt}{}{\sin \frac{\pi }{4}}{\cos \frac{\pi }{4}}=\genfrac{}{}{1.0pt}{}{\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}}=1$$