Trigonometric and Inverse Trigonometric Function Gallery
The following is a gallery of demos illustrating selected families of trigonometric functions These animations can be used by instructors in a classroom setting or by students to aid in acquiring a visualization background relating to the change of parameters in expressions for functions. Two animation file formats, gif and mov are available.
The gif animations should run on most systems and the file sizes are relatively small.
The mov animations require the QuickTime Player (version 6) which is a free download available by clicking here; these files are also small. (The mov files may not execute properly in older versions of QuickTime.)
The collection of animations in gif and mov format can be downloaded; see the zipped download category at the bottom of the following table.
We use abbreviations, GSP for Geometer's Sketch Pad 4, MAT for MATLAB, and EX for Excel spread sheet, to indicate the software used to generate the frames of the animation. If alternate corresponding software is available there will be more than one abbreviation will appear. Software routines can also be downloaded.
Trigonometric and Inverse Trigonometric Functions
Generating Sine MAT 
Gif Animation Mov Animation 

Sine functions f(x) = a sin(b x) + d and f(x) = a sin(b (x+c)) + d GSP also an EXP file 

Vary a:
Gif Animation Mov Animation Vary b:
Gif Animation Vary c:
Gif Animation Vary d:
Gif Animation 
Generating Cosine MAT 
Gif Animation Mov Animation 

Cosine functions f(x) = a cos(b x) + d and f(x) = a cos(b (x+c)) + d GSP also an EXP file 
Vary a:
Gif Animation Mov Animation Vary b:
Gif Animation Vary c:
Gif Animation Vary d:
Gif Animation 

Generating Tangent MAT 

Gif Animation Mov Animation 
Tangent functions f(x) = a tan(b x) + d and f(x) = a tan(b (x+c)) + d GSP also an EXP file 
Vary a:
Gif Animation Mov Animation Vary b:
Gif Animation Vary c:
Gif Animation Vary d:
Gif Animation 

Generating cosecant MAT also a GSP file 
Gif Animation Mov Animation 

Generating secant MAT also a GSP file 
Gif Animation Mov Animation 

Generating cotangent MAT also a GSP file 
Gif Animation Mov Animation 

Generating the inverse sine graph and
function MAT also a GSP file 
The graph: Gif Animation Mov Animation The function: 

Generating the inverse cosine graph and function MAT also a GSP file 
The graph: Gif Animation Mov Animation The function: 

Generating the inverse tangent graph and function MAT also a GSP file 
The graph: Gif Animation Mov Animation The function: 

Zipped downloads ==> 
Download (all) Gif and Mov Animations (large file) Download (9) Geometer's Sketch Pad files 
Other Selected Resources:
A demo that provides a visual development
of the sine and cosine functions and their graphs by 'wrapping' around a
circle is available at mathdemos.org.
Click on Go to
Demo List, then click on Software
Demos, and finally click on 'Circular
Functions'.
At the following BBC education site there
is a very nice interactive applet for generation of sine, cosine, and
tangent graphs by dragging a point around the unit circle. http://www.bbc.co.uk/education/asguru/maths/13pure/04trigonometry/22graphs/22graphs.shtml
At
the following URL there is a nice introductory discussion of basic ideas
including circular
functions, periodic functions,
even & odd functions, and graphs of trigonometric functions.
http://www.pinkmonkey.com/studyguides/subjects/trig/chap5/t0505101.asp
For a nice discussion with accompanying pictures for
the topics of amplitude, horizontal shifts, vertical shifts, and period
changes for sine and cosine go to http://www.krellinst.org/UCES/archive/resources/trig/node44.html
At http://www.univie.ac.at/future.media/moe/galerie/wfun/wfun.html
under the heading Function 2 are applets and recognition puzzles for graphs
of sine and cosine. The recognition puzzles are interactive where you match
figures with equations. A very nice idea.
The Math Archives at http://archives.math.utk.edu/topics/trigonometry.html
has a wide variety of resources connected to trigonometry for various
levels.
Another
source of links to trigonometry applets and information is at http://www.langara.bc.ca/mathstats/resource/onWeb/precalculus/trig/
The
Natural Cosine and Sine Curves — Bob Palais [ JOMA Approved ]
This mathlet illustrates the relationship between the graphs of the natural
(radian measure) sine and cosine curves and the vertical and horizontal
coordinates of points on the unit circle. It can be used in calculus classes
to provide an alternative way of understanding the derivative rules for sine
and cosine.
Credits:
The Geometer's Sketchpad routines were constructed by Mark Yates of The McCallie School.
The MATLAB and Excel routines were constructed by David R. Hill, Temple University.
Special thanks to Deane Arganbright of University of Tennessee at Martin and to Walter Hunter of Montgomery County Community College for their assistance with the development of the Excel files that accompany this gallery. The book "Mathematical Modeling with Excel", by Erich Neuwrith and Deane Arganbright (BrooksCole) provides a rich source of information for developing Excel routines for mathematical instruction.
This gallery was developed by David R. Hill, Temple University.
