Exploration

 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 $f(x) = a\, cos( 2 \pi\, (b x + c) )$ 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. file=Sin-grapher-add_rjk.swf

Amplitude

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 $a\,$ the line remains horizontal and moves up and down with the value of $a\,$. If the value of $b\,$ is changed from zero the line moves back and forth across the x-axis. We like to say it oscillates! If the value of $c\,$ is changed from zero (when $a\,$ and $b\,$ 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?
• $a\,$
• Absolutely correct! The value of $a\,$ determines how high the crests are and how low the troughs are.
• $b\,$
• Incorrect, the value of $b\,$ determines how quickly the sinusoidal wave oscillates.
• $c\,$
• Incorrect, $c\,$ is often described as the phase shift because the wave looks the same except for a shift to the right or left.
• $d\,$
• Incorrect, there is no $d\,$ in the equations $f(x)\,$

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