You should know the sines, cosines and tangents that come from
30-60-90 right triangles and isosceles right triangles. Remember
that $\pi/6$ radians is 30 degrees, $\pi/4$ radians is 45 degrees,
and $\pi/3$ radians is 60 degrees.

DO: Draw the right
triangle with legs of length $1$ and $\sqrt 3$ and hypotenuse of
length $2$. The angle opposite the shorter leg (of
length 1) is $\pi/6$ and the angle opposite the longer leg (of
length $\sqrt 3$) is $\pi/3$. If you memorize this triangle,
you are set, since from this triangle you get all the following
values:

$\sin(\pi/6) = \frac{1}{2};$

$\cos(\pi/6) = \frac{\sqrt{3}}{2};$

$\tan(\pi/6)= \frac{1}{\sqrt{3}}$

$\sin(\pi/4)=\frac{1}{\sqrt{2}};$

$\cos(\pi/4) = \frac{1}{\sqrt{2}};$

$\tan(\pi/4)=1$

$\sin(\pi/3)=\frac{\sqrt{3}}{2},$

$\cos(\pi/3)=\frac{1}{2};$

$\tan(\pi/3)=\sqrt{3}$

From these values, we can figure out the trig functions of common
angles in the second, third and fourth quadrant. It is easy to
use symmetry to do this. These ideas and more are developed in the
following two videos: