Question

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/3), what should be used for Xmin and Xmax? Explain your answer.

Answer 1

@shubhamsrg ?

Answer 2

Help!

Answer 3

@help123please.
@Yating
@Tati_Lee
@kelliegirl33

Answer 4

First, distribute the 2 across the expression enclosed in parentheses.

Answer 5

Is my explanation correct? "The 5 could be ignored because we are finding the domain. Since each period has an interval of 2pi, the minimum possible domains would be 2pi and 0, or [0, 2pi]. When the first period is 0, 2(x-pi/3)=0, x=pi/3. pi/3+2pi=7pi/3. Therefore, the Xmin and Xmax would be [pi/3,7pi/3]."

Answer 6

In the formula it says ...cos2(x...
It is the 2 that counts here.
In general, the period of \(\cos ax\) is \(2\pi/a\).
So the period of your function is \(2\pi/2=\pi\).
If you want to draw two complete periods, you can set Xmin=0 and Xmax=2pi

Answer 7

That's right. The 3 can be ignored as well because it increases the amplitude.

Each period, by the way, is pi, not 2pi.

Answer 8

It is not important that the graph is horizontally and vertically shifted.
2pi is two periods.
If you would set Xmin=200 and Xmax=200+2pi, you'd still get two complete periods

Answer 9

Just think about Ymin and Ymax as well, if you want to be sure the graph is visible :)

Answer 10

Thank you! Is the final answer of pi/3 and 7pi/3 correct though?

Answer 11

yes.

Answer 12

Think about it: 7pi/3 - pi/3 = 6pi/3=2pi, so, yes it's correct!

Answer 13

Here is what I described. Look at the values of Xmin and Xmax.