In these graphs, the asymptotes on the graph tan(x) are always when cos=0. The same thing goes for cot, whenever sin=0 there is an asymptote. On the graph for sec, there is asymptote whenever cos=0. For csc, whenever sin=0 then there is an asymptote. The period for the graphs of sine and cosine are both 2pi. The amplitude for sine and cosine are both 1. Both sine and cosine have amplitudes of 1 and periods of 2pi. However, cosine and sine start and end at different points on the graph.