In This Chapter
Comparing tangent and cotangent
Indicating lines where one curve ends and another begins
Moving a graph up, down, and all around
The tangent and cotangent functions have lots of similarities. You can write both functions in terms of sine and cosine, so they share the same function values in their ratios. One difference between tangent and cotangent is that they don't have function values in the same places for the x-values in their domain — they shift over by 90 degrees. Even though their domains (or x-values) are restricted, tangent and cotangent are the only trig functions with ranges (or y-values) that go all the way from negative infinity to positive infinity. The challenges in graphing tangent and cotangent are in dealing with the domain restrictions and asymptotes (dotted vertical lines used to determine the shape of a curve), as you see in this chapter.
The tangent function can be written as the ratio of the sine divided by the cosine: . (For more information on the tangent function, see Chapters ...