Sin(t) - cos(t) can be rewritten as?

[spj1]

The problem:

sin(t) - cos(t) can be rewritten as ? - The answer is sqrt(2)cos(3PI/4 - t).

there is an equation Re^(xt)cos(bt - angle).
R = sqrt(A^2+B^2)

So i get the following answer:

sqrt(2)(cos(t - 3PI/4)).


Why does the correct answer have the 3PI/4 switched with the t??

 

[Nabeshin]

If you remember the graph of cosine, the property should come to mind that:
cos(-x)=cos(x), which is what's being used here.