http://www.ck12.org Chapter 5. Trigonometric Functions
Notice that the period of tangent isπ not 2 π,because it has a shorter cycle.
The graph of cotangent can be found using identical logic as tangent. It is shown in Example A.
Example A
Graphf(x) =cotx
Solution: You know cotx=tan^1 x. This means that the graph of cotangent will have zeros wherever tangent has
asymptotes and asymptotes wherever tangent has zeroes. You also know that where tangent is 1, cotangent is also
Example B
Graph the functionf(x) =− 2 ·csc(π(x− 1 ))+1.
Solution: Graph the function as if it were a sine function. Then insert asymptotes wherever the sine function
crosses the sinusoidal axis. Lastly add in the cosecant curves.
The amplitude is 2. The shape is negative sine. The function is shifted up one unit and to the right one unit.