The page you are reading is part of a draft (v2.0) of the "No bullshit guide to math and physics."
The text has since gone through many edits and is now available in print and electronic format. The current edition of the book is v4.0, which is a substantial improvement in terms of content and language (I hired a professional editor) from the draft version.
I'm leaving the old wiki content up for the time being, but I highly engourage you to check out the finished book. You can check out an extended preview here (PDF, 106 pages, 5MB).
TODO:
Aplicaitons: SHM Wave eqn Superposition / beats Interference…
consider the funciton psi of x : ѱ(x) = sin(kx), where k is some constant (wavenumber)
what is the wavelength of this wave?
what is ѱ'(x) ?
what is ѱ(x) ?
what is ѱ'(x) ?
see a pattern?
bonus: what is the 1000 th derivative ѱ(x) ?
sin(kx)+sin(kx + d) = 0 for what values of d is the above equation true?
sin(kx)+sin(kx + c) = 2sin(kx) for what values of c is the above equation true?
sin(x)+cos(x) = Asin(x+B) what are the values of A and B ?
sin(x)+cos(x) = Ccos(x+D) what are the values of C and D ?
sin(x+a) = Esin(x) + Fcos(x) What are the values of E and F (expressed in terms of a) ?
Hint: the only thing you need to know to derive all of the above is the following three formulas:
(1) sin^2 x + cos^2 x + 1 (2) sin(a+b) = sin(a)cos(b) + sin(b)cos(a) (3) cos(a+b) = cos(a)cos(b) - sin(a)sin(b)
Eqns (2) and (3) come witha little mnemonic sin –> sico sico cos –> coco - sisi (the negative sign because it is not good to be a sissy)
If you know (1), (2), (3) you kick ass !