Now, how to remember all this AND put it together with sines, cosines, etc:

It's really simple.

There are only five things you need to remember:

1Sine guys are "up and down" guyssine guys go up and down
2Cosine guys are "back and forth" guyscosine guys go back and forth
 

3

The short length is

1 / 2

the short length is 1 / 2
 

4

The medium length is

square root( 2 ) / 2

the medium length is squareroot( 2 ) / 2
 

5

The long length is

square root( 3 ) / 2

the long length is square root( 3 ) / 2