|Play with the 'Unit Circle' definition and how
it relates to the graphs
[Run the Applet]
Note to Students and Teachers:
Note: This applet uses a farily recent version
of Java. As many browsers are not yet up to date, it is set up to use
Plug-in for Java (and will prompt you with how to install it if you
already have it).
This applet explores the 'Unit Circle' definition of the trigonometric
functions and shows how it relates to their graphs.
of the six functions corresponds to the length of a line in the circle
picture as it depends on the length of an arc around the circle - and
the graph color matches that of the corresponding line. If only one of
the six functions is chosen, then extra lines are drawn to help make
clear the equality of line length and graph height. The applet can be
used to get a sense of how the geometric behaviour of the line lengths
relates to the shapes of the graphs and also to understand the
geometric reasons for some of the identities relating different trig
Note to Developers: The applet linked to above was built
the GeX component library which is intended to support the quick
construction of demonstration tools for mathematics instruction.
Copyright 2005 by Alan
Cooper - page last modified on 10 Nov2005