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!

  • 1
    $\begingroup$ $a_0+a_1\cos(x)+b_1\sin(x)+a_2\cos(2x)+b_2\sin(2x)+...a_k\cos(kx)+b_k\sin(kx)$. Increasing the coefficients $a_i$ or $b_i$ increases, roughly, the amplitude. The larger the $k$ for non-zero terms, the larger the frequency of the harmonics involved. $\endgroup$ – OR. Mar 19 '14 at 18:02

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