why do we always use sine wave to represent a wave in amplitude modulation?

Question

i have seen in texts that we al;ways use sin wave to represent a AM modulated wave why dont we use a cosine wave or tangetial wave to do so

Answer 1

Well the tangent function is never used because it is not continuous over more than one period (sinx/cosx = inf if x = pi/2, etc). The cosine wave could be used just as easily as the sine wave, but for generality only the sine function is used (you can get a cosine wave from a sine wave by adding the appropriate phase). So since the sine and cosine waves are basically identical (have same amplitude, and same period, just different phase).

Answer 2

A sine wave looks so elegant and in most of the physical processes, the signal doesn't start with a full amplitude of 1 when time is zero. So, a sine wave represents the real life better than a cosine wave. A tan wave goes to infinity and so is difficult to represent.

Answer 3

textbook wise, it's the easiest way to show the relationship between the real and frequency domain. Remember, Fourier analysis is very important in audio engineering/mathematics. If a more complex method was used it would make subsequent calculations a major pain in the **** and you would eventually have to shift back to a harmonic function (solves the laplace equation) anyway.

It also makes power determination easier: eg: Paley -Weiner criterion etc.

Answer 4

enable Acos(t) + Bsin(t) = Rsin(t + x) boost the RHS: Rsin(t + x) = Rsin(t)cos(x) + Rsin(x)cos(t) Equate coefficients: cos(t) : Rsin(x) = A sin(t) : Rcos(x) = B sq. the two equations, and use sin^2(x) + cos^2(x) = a million R^2 = A^2 + B^2 R = root(A^2 + B^2) Divide good equation by making use of backside equation sin(x) / cos(x) = A/B tan(x) = A / B x = arctan(A/B) consequently: Acos(t) + Bsin(t) = (root(A^2 + B^2)) * sin(t + arctan(A/B)) Sine wave with era 2pi :) Amplitude is R and area is the arctan(A/B)