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 !