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Math review
AC currents are all about the sin function, its amplitude and its phase. This is a little question-based referesher course on the sin and cos funcitons. Q1. 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) ? Q2. sin(kx)+sin(kx + d) = 0 for what values of d is the above equation true? Q3. sin(kx)+sin(kx + c) = 2sin(kx) for what values of c is the above equation true? Q4. sin(x)+cos(x) = Asin(x+B) what are the values of A and B ? Q5. sin(x)+cos(x) = Ccos(x+D) what are the values of C and D ? Q6. 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 !