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Calculus IV
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S = contains supplemental resources
Course: Trigonometry
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:

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

Download: Graphs of Six Trig Functions and Basic Information
Note the graphs are in blue with one period of each marked in bold blue. Asymptotes are in red. The last two functions show the sine and cosine graphs in green only for reference.

Check out the connection between the unit circle and the graph of the sine, cosine, and tangent functions at Interactive Unit Circle from Math Is Fun. As you drag the point around the unit circle, watch the length of the red "height" line defining the "height" of the sine function and the graph of a sine wave spin out. You can do similarly for the blue cosine function and green tangent function. Cool connections to understand, strongly recommended interaction!

If you prefer to see them separated check out Unit Circle and Sine Graph and Unit Circle and Cosine Graph each from GeoGebra.

A similar, but more complex, Java-based example is shown at Sine Wave Geometry from Dynamic Geometry.

For the other trig functions and their connection to the circle, see Graphs of Tangent, Cotangent, Secant, and Cosecant from Interactive Mathematics.

You may also want to read Intuitive Understanding of Sine Waves from Better Explained but it is completely optional.

Supplemental Resources (optional)

Videos from James Sousa's MathIsPower4U:

Mini-Lesson: Graphing the Sine and Cosine Functions
Animation: raphing the Sine Function Using the Unit Circle
Animation: Graphing the Cosine Function Using the Unit Circle
Example: Graph the Sine Function Using the Unit Circle

Mini-Lesson: Graphing Cosine, Sine, and Tangent on the TI84
Mini-Lesson: Graphing the Tangent Function
Animation:  Graphing the Tangent Function Using the Unit Circle
Mini-Lesson: Graphing Tangent and Cotangent over different Periods
Example: Graphing the Tangent Function Using the Unit Circle and the Reciprocal Identity
Example: Graphing the Tangent Function Over a Different Period

Mini-Lesson: Graphing the Cosecant and Secant Functions
Mini-Lesson:Graphing the Cotangent Function
Mini-Lesson:Graphing Secant, Cosecant, and Cotangent on the TI84
Example: Graphing the Secant Function Using the Cosine Function
Example: Graphing the Cosecant Function Using the Sine Function