Back to . . . . Curve Bank Home  NCB Deposit  # 26 The Students of CS 390  Software Architecture The Two Most Studied Curves in Trigonometry The Sine and Cosine Functions An oscilloscope traces the sound wave of a recorder.

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 Significance Many different physical phenomena may be measured by their wave motion.  Perhaps the best known examples are those of radio waves, television waves or microwaves.    Indeed, radio stations are named for their types of wave transmission.  For an AM station, the  amplitude of the wave is varied to carry different sounds.  An FM station has its  frequency modified.  Thus, AM stands for  amplitude modulation and FM represents frequency modulation. The difference may be illustrated using the sliders on the above graphic.

 Observation: Any book on trigonometry will have these two, much studied functions.  However, in the physical sciences where math is often applied, the sine function, or cosine function may be "squared."   The  x value often represents time and the  y value, i.e., the function value, is the periodic signal being studied.  In the case that the sine or cosine function is "squared,"  the student may recognize this as being similar to the  "piecewise" function, or "step" function studied in earlier algebra courses. The more advanced student will also recognize the function as an expanded Fourier series with a periodic cycle. Students will recognize a familiar  piecewise function from Pre-calculus  can easily be applied to time and a time  function.
 Links and Printed References Animated Unit Circle  <  http://curvebank.calstatela.edu/unit/unit.htm  > Another animated Unit Circle  < http://curvebank.calstatela.edu/sine/sine.htm  > Square Functions and other Fourier applications for the advanced student.  See  < http://www.falstad.com/mathphysics.html  >. John Johnson, Jr.,  "COLUMN ONE: Gravity's Field of Dreams," Los Angeles Times, June 10, 2006, p. 1. Donald A. McQuarrie,  MATHEMATICAL METHODS  for Scientists and Engineers, University Science Books,  Sausalito, CA, ISBN 1-891389-24-6, 2003.