5.7. Graphs of Other Trigonometric Functions http://www.ck12.org
Note that only the blue portion of the graph represents the given function.
Example C
How do you write a tangent function as a cotangent function?
Solution: There are two main ways to go between a tangent function and a cotangent function. The first method
was discussed in Example A: f(x) =tanx=cot^1 x.
The second approach involves two transformations. Start by reflecting across thexor theyaxis. Notice that this
produces an identical result. Next shift the function to the right or left byπ 2. Again this produces an identical result.
f(x) =tanx=−cot(x−π 2 ).
Concept Problem Revisited
The four new functions are not purely transformations of the sine and cosine functions. However, secant and
cosecant are transformations of each other as are tangent and cotangent.
Vocabulary
Atransformationis one that preserves the essential nature of the original graph. It does not introduce discontinuities
or change the ordering of the points. Examples of transformations are stretching, reflecting and shifting.
Guided Practice
- Find the equation of the function in the following graph.