Using the table above I was able to make the graphs shown in the picture below.
Period and Amplitude
Tan Graph: The amplitude in the tangent graph is none, the graphs go on forever in both directions. The period of the graph is pi.
Cotangent Graph: This graph has the same amplitude and period as tangent.
Cosine Graph: The amplitude for cosine is one and the period would be 2pi.
Secant Graph: The amplitude is none because they go on forever. The period is 2pi.
Sine Graph: The amplitude is one and the period is 2pi.
Cosecant Graph: The amplitude in the cosecant graph is none, they go on forever. The period is 2pi.
Tan Graph: The amplitude in the tangent graph is none, the graphs go on forever in both directions. The period of the graph is pi.
Cotangent Graph: This graph has the same amplitude and period as tangent.
Cosine Graph: The amplitude for cosine is one and the period would be 2pi.
Secant Graph: The amplitude is none because they go on forever. The period is 2pi.
Sine Graph: The amplitude is one and the period is 2pi.
Cosecant Graph: The amplitude in the cosecant graph is none, they go on forever. The period is 2pi.
Compare and Contrast
The cosine and sine graphs look the same except the sine graph passes through (0, 0) and cosine has a point somewhere on the y-axis.
Vertical Asymptote
For tangent and cotangent the vertical asymptote is at the end of each cycle. Cosecant has a vertical asymptote that occurs at pi and repeats every pi units. Secant has a vertical asymptote that occurs at pi/2 and repeats every pi units.
For tangent and cotangent the vertical asymptote is at the end of each cycle. Cosecant has a vertical asymptote that occurs at pi and repeats every pi units. Secant has a vertical asymptote that occurs at pi/2 and repeats every pi units.