1. For transformations I remember it in several ways. For example when it is (x-5), you would move the graph left 5 units. It's pretty much always the opposite of what it looks like.
Another example would be (x-5) -7. In this equation you already know to shift it left 5 but then what about the -7 outside of the parenthesis. The number outside makes it shift vertically down 7 units.
2. For trig its all about memorizing and utilizing the unit circle. For the 4th quadrant I remember that you have to multiply by 2 and then subtract 1. Thats an easy way to remember it. The zeros are the easiest thing to remember on the circle, they are (1,0) (0,1) (-1,0) (0,-1). In quadrant 1 all the values are positive. Also for the unit circle an easy tip to remember is that most of it is just mirrored. For example the numbers 6 4 3 2 are all mirrored.
3. One thing that still confuses me is how to graph the sin and cos. Also how to graph the inverse. I still don't understand it.