you should read the question, it doens't seem to hard, really its pattern matching.
K * TRIGFUNC( (2pi/T)t - Phi ) + Vert
K -- amplitude
T -- period
Phi -- phase (you may want to "bound" the phase, force it be be between -pi and pi)
Vert -- vertical offset (aka DC offset)
* might be + Phi.
now for csc, tan, ctn, sec, you may need to put amplitude as inf, as these all have asymtotes.
graphing is also equally easy. CSC is 1/COS. so any point COS = 0, CSC = inf and -inf (an asymtote). if COS = 1, CSC = 1.