Maxima of Cosine Functions with Integer Values of Y

[d6syxx]

For what values of y are the maxima of the functions cos(x-y) and -cos(x) located at the same x values?
(n/2), where n is an integer
(1+n/2), where n is an integer
(2n+1/2), where n is an integer
n , where n is an integer
(2n+3/2), where n is an integer
2n, where n is an integer
(2n+1), where n is an integer
(n+1/2), where n is an integer

I'm no physicist, but in order to graduate I need to take physics. I skipped Trigonometry and went straight to calculus, learning whatever Trig I needed to pass the class. I feel I made a horrible mistake because I can't do this problem or any problems like it. If anyone is willing to help me I would be much appreciative and even offer a cash bonus to anyone that is willing to do so. I have several problems similar to the one above. Thanks.

 

[Hootenanny]

Note that;

$$\cos(A-B) = \cos(A)\cos(B)+\sin(A)\sin(B)$$

P.S. This is probably better placed in PreCalc math

 

[d6syxx]

I know that, but how does that relate to this problem?

 

[Hootenanny]

Well, where are the maximas of -cos(x) located?

 

[d6syxx]

I have no idea! 1?

 

[Hootenanny]

Okay, what are the x values for when -cos(x)=1 (I'll give you a clue, there's only one)

 

[d6syxx]

2pie or zero?

Are you saying, where does the -cos of x = 1? Like on a unit circle?

 

[Hootenanny]

2pie or zero?

Close, that would be the cases where cos(x)=1

Are you saying, where does the -cos of x = 1? Like on a unit circle?

Yes, or in other words, where does cos(x)=-1

 

[d6syxx]

In that case, it would be Pie