Why a sinusodial signal expressed by a cosine function instead of a sin function?
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.