Topic: Graphs of Trigonometric Functions
Subtopic: Basic Graphs
Overview
We have studied the trigonometric functions from an algebraic perspective, but today we begin to study and analyze their graphs. This chapter is graph intensive. You should have your electronic grapher ready so you can follow along. If you have any trouble producing the graphs on your grapher, please ask questions in class.
Objectives
By the end of this topic you should know and be prepared to be tested on:
- 4.1.1 Be able to graph the six basic trig functions (algebraically and electronically)
- 4.1.2 Know the domain, range, asymptotes, amplitude, period, and symmetries of the six basic trig functions
Terminology
Define: domain, range, asymptote line, amplitude, period, symmetry, line of symmetry, symmetry (about x-axis, y-axis, origin, line y=x), odd function and even function (graphically; relation to symmetry).
Supplementary Resources
Check out the connection between the unit circle and the graph of the sine function Unit Circle to Sine Wave from CiteJournal.org. As the unit circle gets spun out, watch the green "height" line defining the "height" of the sine function. Think about, in a similar way, what might be the connection between the unit circle and the cosine function. A similar, but more complex, example is shown at Sine Wave Geometry from DynamicGeometry.com.