Trigonometric functions are sometimes called circular functions. This is because the two fundamental trigonometric functions the sine and the cosine are defined as the coordinates of a point P travelling around on the unit circle of radius 1 .
As P moves around the circle of radius 1, the input variable the angle q changes. The outputs
Review of angular measure
Methods for finding sines & cosines
This gives us a clue about the kinds of phenomena that trigonometric functions are likely to model. Going around in a circle is a very simple kind of periodic behavior. Periodic behaviors repeat themselves at regular intervals. The sine and the cosine repeat their outputs at regular intervals. Indeed, each time P travels once around the circle (the input q changes by 2p radians or 360º) the coordinates of P (the outputs of sine and cosine) repeat.
By changing the size of the circle and the speed at which the point P travels around it, transformations of the sine and the cosine can be made to model a wide variety of regularly repeating behaviors.
Trigonometric functions model data with periodic trends.
Here are some situtations that should make you think of trigonometric functions:
Words and phrases like "seasonal," "repeatedly," and "over and over" usually indicate the presence of trigonometric functions.
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