It simple! Lets if my equation is y=2sin(2x). First I would want to establish my zeros. They would at the origin, pie and in the middle at pie over 2. Next, you would place your max and mins. The first would be a max at positive 2 and the next one would be a min and -2; you would keep alternating until you run out of graph space.
Ok, what about sin?
Its pretty much the same thing as sin. If it was the same equation as sin. The period would stay the same but the zeros would be moved up 2 on the y-axis. The max and mins would be at 4 and 0 on the x-axis.
Ok, so for tan, if the equation is y=tan1/2x you would want to start by plotting the zeros because the period is 2 pie, the zeros would be placed at pie and 2 pie. At those points, you would draw a dotted line called an asymptote. These are like borders and the line that you would draw cannot pass it. Between the zeros, you would place your point to start the line (at the origin). Finally, you would place the final two points over 2 places and up one. Now you just connect your lines.
Now, what about tangent?
No problem, if you ever need any help.....I gotch you.