Is a voltage signal we observe on scope made up of only cosines?
Both the cosine and the sine part of the complex \$e^{j\omega t}\$ function hold exactly the same information. Choose all cosine or all sine (and multiply with -j to get real) and you are fine. Just don't mix cosine and sine, as that results in complex gibberish.

The reason why cosine is often preferred for the representation is because it's invariant to negative time. \$f(-t)=f(t)\$ Because the cosine is axis-symetrical. In contrary, sine would require you to invert the result for negative time.