You know definitions of sine, cosine, and tangent. Cosecant, secant, and cotangent are reciprocals of those functions, respectively. Study the graph below. It offers a different view into some of those functions.
For each marked, colored segment, explain why it represents the function it claims it does.
Graphs of sine and cosine should be second nature. Tangent should be pretty close. The other three are little less used, but should be familiar. For each of the other three, explain how you would graph them, using sine, cosine, and tangent. Then say everything you can about their properties without graphing them first: intercepts, asymptotes, limits.