The Simulation

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Explore the Equation grapher simulation (below) for several minutes:
  • The axes of the graph are indicated by black lines and labels x and y.
  • The black "tick" marks represent a magnitude of 1 from the origin (0,0).
  • The sinusoidal function [math] f(x) = a\, cos( 2 \pi\, (b x + c) ) [/math] is represented by the red line.
  • Try clicking check boxes
  • Try sliding sliders
  • Try entering number in textboxes

When you have finished exploring try the multichoice question. Once you have completed the multichoice question try one of the main activities.


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While you were exploring you may have noticed that the function starts as a horizontal line along the x-axis. If you only change the value of [math]a\,[/math] the line remains horizontal and moves up and down with the value of [math]a\,[/math]. If the value of [math]b\,[/math] is changed from zero the line moves back and forth across the x-axis. We like to say it oscillates! If the value of [math]c\,[/math] is changed from zero (when [math]a\,[/math] and [math]b\,[/math] are not zero) the crests and troughs moves side to side sometimes crossing the y-axis.

  • What parameter best describes the amplitude of the wave?
    • [math]a\,[/math]
      • Absolutely correct! The value of [math]a\,[/math] determines how high the crests are and how low the troughs are.
    • [math]b\,[/math]
      • Incorrect, the value of [math]b\,[/math] determines how quickly the sinusoidal wave oscillates.
    • [math]c\,[/math]
      • Incorrect, [math]c\,[/math] is often described as the phase shift because the wave looks the same except for a shift to the right or left.
    • [math]d\,[/math]
      • Incorrect, there is no [math]d\,[/math] in the equations [math]f(x)\,[/math]

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Tip: You might want to have a look at the definition of amplitude