sine, cosine and tangent are angle functions that will let you find out angles in a right angled triangle if you know the length of the sides, and vice-versa. However in programming they are more useful for creating nice smooth waves, and plotting circular paths for objects. As an angle increases from 0 to 360, sin and cos will make a wave pattern from 1 to -1, and you can use this to make kind-of smooth hills, if you set the matrix height to the sin of an angle. Of course since the functions only produce numbers between 1 and -1, you will have to multiply the sin of an angle by a coefficient to get any noticeable effect.

This code will prodice a sine wave:

for i=0 to 360
dot i,480+(sin(i)*100)
next i

and a cos wave (basically a sin wave moved on by 90 degrees)

for i=0 to 360
dot i,480+(cos(i)*100)
next i

Normalisation is hard, I couldn't get my head round it when I tried to do it.

I never realised how hard it is to explain the usefulness of sin and cos, I use them fluently in just about every program I make, but trying to explain them to someone else is really hard. It's probably too late at night to explain anything useful.