The "law of cosines" can be used to find
the third side of any triangle if you know the first two sides and the angle
between them. This fact also helps derive relationships between sin and
cos of different angles, such as
sqrt(2-2cos x) = 2 sin(x/2)
Sines and Cosines of Common Angles
gives a method for first year trig students to breeze through the homework and
test questions having to do with sines and cosines of common angles -- all the
multiples of 30� and all the multiples of 45� in every quadrant.
Trig Equivalences are handy. Some
have proofs.