If the instructions for a problem ask you to use the smallest possible domain to completely graph two periods of y = 5 + 3 cos 2(x - pi divided by three), what should be used for xmin and xmax? explain your answer.

The correct given equation is:

y = 5 + 3 cos 2 (x – π/3)

 To answer this problem, we must remember that:

y = A cos [w(x - π)], the period is 2 π / w and the phase shift is π (the beginning of one period)

Rewriting the given equation to this form,

y = 5 + 3cos [2(x - π/3)] 

Therefore,

period = 2 π / 2 = π
phase shift = π /3 

So to create two periods, you need an interval of 2 π
If you start at π /3, you'll start and end at the max of the cos function.

Therefore,

 [Xmin , Xmax] = [π /3 , 7 π /3] would create a complete graph of 2 periods.

ANSWER: [π /3 , 7 π /3]

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