Reciprocal Functions vs. Standard Functions

Unlike normal sine or cosine functions, these reciprocal functions have asymptotes. For cosine functions, to find the asymptotes at x= /2+n, where n is an integer and the cosine function is 0 at these x values. Similarly for sine functions have asymptotes when sinx=0 and that is at x= n. To sketch these functions, you should first graph the reciprocal function, the sine or cosine function. For example if you are trying to sketch y=cscx, first sketch y=sinx. Then take the reciprocals of the y coordinates to obtain points on the graph of y=cscx.

The blue line is y=sinx
The Black line is y=cscx
The dotted lines are the asymptotes at and 2

COT vs TAN

Cotangent functions have similar graphs to tangent functions. They both have a period of . The major differences are that the graph of the function is reversed and that instead of having a domain of – /2 to /2, it has one from 0 to .