If I were to turn f(x) = 3 cos(2x) + 4 sin(2x) into a single function... Where would I want to start? Would I just use the double angle formulas and go from there?
f(x) = 3cos(2x) + 4sin(2x) = 3(cos^2(x) - sin^2(x)) + 4*2sin(x)cos(x)
As it happens you can factor this:
f(x) = [3cos(x) - sin(x)][cos(x) - 3sin(x)]
But that doesn't give you the form you want.
If you mean can you get it just in terms of sine or cosine, THAT we can do:
Basically, look at the graphs show below.
Topsquark, you should define a function,
that is if otherwise
Then you can say,
I actually think my function can be useful. Look at the Heaviside function.
Can you express my function as a fourier series or will it lead to Gibbs phenomena?
I would know we don't have the stereotyped math sequence that you
seem to have in the US).
The only things you need to know to do it is the sin addition formula and
the trig form of Pythagoras's theorem, which are:
and the rest is just basic algebra.