For both I don't agree with how this way said. True, the secant and tangent functions already have a range of -infinity to infinity, but I have a hard time calling that 3 in front of the tangent as anything other than an amplitude. (There is technically a multiplicative factor of "1" in front of the secant as well.) I suspect there is no standard term for the 3, except maybe a "dilation."

For the periods let's take the secant function first. Assume a value of X such that the function starts to repeat itself. The secant function repeats itself every 2*pi radians. Thus 3X = 2*pi. etc.

The tangent is a bit trickier, but the same method applies. tangent repeats itself every pi radians. (If this seems odd, graph it.)

-Dan