Today in class we started by reviewing the basic facts about the graphs of y = a cos (bx) and y = a sin(bx). We moved on to an example of writing an equation for a given trig graph. You need to consider how to find the amplitude (a = (Max - min) / 2), the vertical shift (k = (Max + min) / 2), and b by recognizing the period (period = 2π / b). Once those values are determined, consider the graph of y = a cos (bx) + k. Finally, determine how that graph can be shifted to "overlap" the given graph to obtain a final equation of the form y = a cos(b(x - h)) + k.
The same process can be used to obtain an equation of the form y = a sin (b(x - h)) + k. Note, there is not one unique answer in any case.
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