Graph the function in the TS plane, where T axis is horizontal, S axis vertical. What is the period of the function? What symmetry does the graph have? Let's recall that Y equals tangent. X is a graph that looks like this, with asymptotes at π halves and at negative π halves, and it continues on. So we could put in multiple periods if we wanted three Pi halves in a unit circle. The tangent values repeat. If you think about it's a positive and then a negative and then a positive then a negative. It takes one full π cycle to get through all the positive and negatives before that cycle repeats. So here's a positive and a negative again. So the period is going to be π for a plain old tangent X. But when there's a coefficient like a 2IN front, what we do is we take the period and we divide it by whatever that constant is. So in this case. Divided by two regular. For tangents π so π / 2 and then we wanted to know where it's symmetric about. It is symmetric about the origin. If we thought about picking it up and rotating at 180°, it would look just like itself. Or F of negative X = -F of X. That's another way of saying that it's symmetric around the origin.