This applet explores the 'Unit Circle' definition of the trigonometric functions and shows how it relates to their graphs. Each 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 functions. |
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