I found the following question and wonder what the subject of this material is called and how you actually solve that (what method do you use?). I can't seem to find the name anywhere even though I have been searching.
If you are given
and
how do you find $A_2$, $ω_2$ and $φ_2$ so that the function $f_2(t)$ can be written on the following form:
EDIT: Another example look like this:
Find the constants $A_1$, $ω_1$ and $φ_1$ so the following is satisfied:
Basically, you have to use trigonometric identities to get a new expression for your function.
Hint:
We have $$ \forall t, f_2(t) = 5 \times \sin(\frac{\pi}{2}t + \frac{\pi}{4} + \frac{\pi}{2} - \frac{\pi}{2}) = 5 \times \cos(\frac{\pi}{2}t + \frac{\pi}{4} - \frac{\pi}{2}) $$