In the signals and systems course one of the first things that we see is a sinusodial signal wave. And they say its expressed like \$A\cdot\cos(\omega t + \phi)\$. But why we use a cosine function when we work on a sinusodial signal? why its not \$A\cdot\sin(\omega t + \phi)\$?
for example: http://users.abo.fi/htoivone/courses/sigbe/sp_sinusoidal.pdf
or watch the first minute of this video: https://ocw.mit.edu/resources/res-6-007-signals-and-systems-spring-2011/video-lectures/lecture-2-signals-and-systems-part-i/
Best Answer
A cosine and sine wave are essentially phase-shifted versions of one another. For instance,
\begin{equation*} cos(x+\phi) = sin(x+\phi-90) = sin(x+\theta) \end{equation*}
where
\begin{equation*} \theta = \phi-90 \end{equation*}
Hence, a cosine and sine wave are essentially the same, and what differentiates their use is the value of the initial phase.
However, a primary reason as to why the cosine notation is preferred is because of the frequent occurrence of complex envelopes in the area of Signals/Systems. An example of the use of complex envelopes is when a sinusoid of low frequency, say m(t), is modulated onto a sinusoid of higher frequency (fc); the resultant modulated signal r(t) can be expressed as:
\begin{equation*} r(t) = Re\{m(t)e^{j 2 \pi f_{c} t} \} \end{equation*}
As it turns out, the real part of a complex envelope is a cosine waveform (Refer to Euler's formula) and hence it is much more convenient to represent a signal, such as r(t), using a cosine.