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.

1. The gif animations should run on most systems and the file sizes are relatively small. 

2. 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.) 

3. The collection of animations in gif and mov format can be downloaded; see the zipped download category at the bottom of the following table.

4. 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                Mov Animation Vary c: Gif Animation               Mov Animation Vary d: Gif Animation               Mov 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                Mov Animation Vary c: Gif Animation                 Mov Animation Vary d: Gif Animation               Mov 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               Mov Animation Vary c: Gif Animation                Mov Animation Vary d: Gif Animation               Mov 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:       separate graphs Gif Animation                                 Mov Animation       single graph       Gif Animation                                 Mov Animation
Generating the inverse cosine graph and function MAT also a GSP file		The graph: Gif Animation                   Mov Animation    The function:       separate graphs Gif Animation                                 Mov Animation       single graph       Gif Animation                                  Mov Animation
Generating the inverse tangent graph and function MAT also a GSP file		The graph: Gif Animation                     Mov Animation    The function:       separate graphs Gif Animation                                  Mov Animation       single graph       Gif Animation                                      Mov Animation
Zipped downloads ==>	Download (all) Gif and Mov Animations (large file) Download (12) MATLAB files Download (9) Geometer's Sketch Pad files Download (3) Excel 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 (Brooks-Cole) provides a rich source of information for developing Excel routines for mathematical instruction.

• This gallery was developed by David R. Hill, Temple University.

8/6/03DRH          Last updated  5/22/2006 As of 8/29/03