Posted by kate on Thursday, December 17, 2009 at 10:07pm.
Are you referring to the trigonometric functions? Namely sin, cos, tan, csc, sec, and cot that make up the first 6, and their inverses that make the other 6?
It would be a good exercise to sketch each of the three basic functions (sin, cos, and tan) to familiarize yourself with the nature of these functions, if this was not already done in class by your teacher.
The functions csc, sec and cot are the reciprocals. The reciprocals go to zero whenever x approaches 0.
The graphs of inverses poses an extra challenge. Since inverses of periodic functions exist for a particular interval, so the sin, cos and tan functions have to be reduced to a monotonic function that covers the range. For example, for sin(x), the interval chosen is -π/2 to π/2. For cosine, it is from 0 to π. For tangent, the interval chosen is from -π/2 to π/2.
From there, you can deduce the graph of the inverses by reflection about the line y=x.
If you use the textbook Precalculus by Stewart,Redlin and Watson, you can find a lot of information in Sect. 7.4 between pages 550-557.