One possible extension of the problem would be to investigate what happens to the standard sine graph if you add a constant d to the sine function.

Vary d as you nvestigate graphs of the form:


The constant d translates the sine graph along the y-axis. If d is positive, the graph shifts up the y-axis by d units. If d is negative, the graph translates down the y-axis by .

Below is an example to illustrate this movement of the sine graph. The standard sine graph y = sin x is shown in red and the graph of y = sin (x) +4 is shown in blue. Watch an animation of the graph of as d varies between -10 and 10.


Another extension is to investigate similar properties with the graph of y = cos x. What happens to the graph of:

as the values of a, b, and c change?

Below is the graph of the standard equation of y = cos x. Explore and make comparisons on your own as you vary a, b, and c. How do the changes with the cosine graphs relate to the changes with the sine graphs?

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