As you might expect, the sum of two equal-frequency real sinusoids is itself a single real sinusoid. Table 1 gives the sum of two arbitrary cosine functions. Table 2 gives the sum of two arbitrary sine functions. Table 3 gives the sum of an arbitrary cosine and an arbitrary sine function.

All sinusoidal signals have the same general shape, but they are not identical. The three characteristics that separate one sinusoid from another are amplitude, frequency, and phase. Amplitude specifies the maximum distance between the horizontal axis and the vertical position of the waveform.

It is the LCM of the 2 periods, which is 4pi.

The equation of a basic sine function is f(x)=sinx. In this case b, the frequency, is equal to 1 which means one cycle occurs in 2π. If b=12, the period is 2π12 which means the period is 4π and the graph is stretched.

As it turns out, as you might expect, the sum of two equal-frequency real sinusoids is itself a single real sinusoid. Table 2 gives the sum of two arbitrary sine functions.

Adding two sinusoids of the same f’requency but ditl’erent amplitudes and phases results in another sinusoid (sin or cos) of same fiequency. The resulting amplitude and phase are different from the amplitude, and phase of the two original sinusoids, as illustrated with the example below.

Graphs of Sinusoidal Functions The sinusoidal function family refers to either sine or cosine waves since they are the same except for a horizontal shift. This function family is also called the periodic function family because the function repeats after a given period of time.

A curve similar to the sine function but possibly shifted in phase, period, amplitude, or any combination thereof.