Given a function such as \begin{equation*} \cos (x) + 4 \sin (3x) + 5 \cos (3x) \end{equation*} when graphing it to produce a wave, are there any set rules to how you can adjust the function to produce a higher frequency, or increased amplitude, or any other wave properties.
I'm looking for an answer such as "if you change this part of the function you should expect to see _______ changes in the graphed wave".
How would I make the wave spike? How would I increase the frequency? How would I increase the amplitude?
Anything like that! - Hopefully somebody knows what i'm rambling on about, thanks in advance!