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 30º and all the multiples of 45º in every quadrant.
Trig Equivalences are handy. Some
have proofs.
A proof that of rectangles that have a
given area, the square has the smallest perimeter.
A method for finding equations of lines that
pass through points, have certain slopes, or are either parallel or
perpendicular to other lines.
This one is really neat: Can you find an algorithm to tell whether a given
point is inside or outside of a given triangle? It's surprisingly hard to
do, but surprisingly simple once it's done. Check
it out!
