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kirza4 [7]
3 years ago
9

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.
Mathematics
1 answer:
Scrat [10]3 years ago
4 0

The correct given equation is:

y = 5 + 3 cos 2 (x – π/3)

<span> To answer this problem, we must remember that:</span>

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<span>
phase shift = π /3 </span>

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

Therefore,

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

 

ANSWER: [π /3 , 7 π<span> /3]</span>

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