TIP$ AND HINT$

1.- Regarding transformations I try to do them by remembering the parent function. After that I see which part of the function has been "transformed" either the input or the output.
To know if the input is the one altered, I look for any number inside the parenthesis where x is like (2x) or (x+2) . Then the changes for input I know they can only be horizontally or from left to right or right to left because we are playing with the input, which is x, the x-axis.
Sometimes, there might not be a parenthesis and there'll be something like this: f(x)= x+1 so in that case I know that the output is the one being changed because it's not inside a parenthesis.

To know if the output is the one changed I look for numbers around the parenthesis, meaning outside of it
for example: -f(x)=(x), y= 3sin(3x) or y= 2sin(x)+3
The changes for the output I know they'll be vertically because we are playing with the output which is y, the y-axis.
However, there'll be times where there is no ( ) and just something like this : y= 4sin, and still the output is the altered one because it's not inside a ( ) with the x.


2.- Regarding trigonometry, I remember it because I memorized the unit circle. I kind of get confused with the points of π/6 and π/3 but I tried to remember them just by memorizing cosine of one of them, so I'll know that, for example the cosine of π/3 , which is 1/2 will be the sine of π/6 because they switch. Hope I didn't confuse some of you..but that's how I get to remember it,, :).
Also for tanx and cotx, at first I had trouble remembering which was on top so I just said that tanx is the original one so it obeys the rise/run for the slope , therefore tanx will sine/cosine (y/x) and since cotx is the "fake one" (for me) , it'll be the opposite cosine/sine (x/y).

3.- One thing that I still have a hard time doing is the graphing of the trigonometric functions and it gets worst when they have all of the vertical and horizontal transformations because I just get stuck and I don't know where to start. Also, when they have all this transformations I have to have certain points on the x-axis in order to graph them and I don't know which are the right ones to put. I need a tip for this in order to make it easier. I would like to know how to start graphing this and which points I should put on the x-axis :

y= -3tan(3x+π)+2 Help please!