Section TRIG Trigonometric Functions
8.1 Composition
8.2 Roots - Estimation with Linearity
Introduction: All the functions
that are studied can be combined with either
arithmetic operations or composition using a finite or limiting process.
The main class of functions that result from using a finite number of
these processes applied to a list of core functions were characterized
as elementary functions by Euler. These include the rational functions,
the rational power functions, exponential and logarithmic functions, and
the trigonometric functions with their inverses.
This section will provide examples, explanations,
exercises
and problems that will help students use the power of the
mapping diagram along with the three other tools
(equations, tables , and graphs) to understand some of the
more common elementary functions that involve the interactions of
some different types of core functions sometimes encountered in
precalculus and calculus courses.
TRIG.TRIGI Trigonometric Functions are Important. (Not Yet Done)
The following example presents the sine function $\sin(x)$ and the
cosine function $\cos(x)$ with a table of data, a graph and a mapping
diagram for each.
Example TRIG.0
The First Trigonometric Functions Example [Graphs and Mapping Diagrams].
Definition TRIG.DEF : Trigonometric Function Definitions
Definition TRIG.INV: Inverse Trigonometric Function Definitions
Treatment of trigonometric functions and their graphical interpretation are familiar. [See wikipedia.org/wiki :trigonometric_function]
They appear in every textbook that deals with trigonometry and preparation for calculus. What is missing is a balanced treatment using mapping diagrams to reinforce the function aspect of visualization. That will be emphasis of this section.
Comparisons will be made when appropriate to graphs- but we will develop the basic concepts for trigonometric functions with mapping diagrams. The end of this section includes some powerful and different ways to think about trigonometric functions and the ways they are represented algebraically.