This site contains a graphical introduction to trigonometry through Flash-animated lessons, many of which incorporate audio. It includes an overview of the graphs of the six basic trigonometry functions, the laws of sines and cosines, and graphics relating degrees and radians. It also allows students to
grasp the concept of how the unit circle relates to the graphs of trig functions. This site is a work in progress.
Type of Material:
These 10 lessons could be used by a trigonometry student who needs a visual tool to get a more solid understanding of the trig functions and the laws of sines and cosines.
Identify Major Learning Goals:
To attain an elementary understanding of the six trigonometric functions, the laws of sines and cosines, and degree and radian measurements.
Target Student Population:
High school and college in a trigonometry or precalculus class.
Prerequisite Knowledge or Skills:
Beginning algebra and some geometry.
The lessons include text that explains the definitions of the six trigonometric functions. The text is accompanied with audio that is synchronized with the text. Along with the text and audio there are graphics and graphical animations that relate the unit circle to the values of the trigonometric functions and their graphs. Lessons 5 through 8 include animations that graphically demonstrate the proofs for the laws of sines and cosines.
In the introductory lesson, csc, sec, and cot are named as reciprocals of sin, cos, and tan, but in lesson 4B, they are called inverse functions. In lesson 2, a negative is used in front of the horizontal variable: -c; in the same lesson, on the same page in the lower right-hand corner of the screen, a positive c is used in the trigonometric functions. This will result in incorrect values for these ratios.
Potential Effectiveness as a Teaching Tool
A wonderful animation tying the trigonometric ratios on the unit circle to the graphs of their functions. The appropriate segment from the unit circle diagram is moved as a vertical strip whose upper endpoint is the point on the graph of the trigonometric functions. This is a creative approach to demonstrating the how the graphs are obtained.
Most students are introduced to the trigonometric relationships using the terms adjacent, opposite, and hypotenuse. No reference is given tying these common terms to the explanation given. Because of this, the site should be used as a reference after an instructor has presented the content, especially for those lessons with no audio components.
Ease of Use for Both Students and Faculty
Very easy to navigate. The graphs and animations are color coded and there are controls to step forward and back through the animations.
Some lessons have no audio component. For the novice student, understanding the lessons with animation only may be difficult. The multitude of information on a single screen can be overwhelming. For more than one reviewer, this site would not open in a Firefox browser even after the most current Flash plug-in was downloaded.
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