Quote by dimension10
I think this is not possible. Maybe your friend considers
[tex]\sin\theta=\frac{{e}^{i\theta}{e}^{i\theta}}{2i}[/tex]
[tex]\cos\theta=\frac{{e}^{i\theta}+{e}^{i\theta}}{2}[/tex]
to be definitions of sine and cosine?

Assuming we're allowed that definition of cosine, then that also works.
Quote by dimension10
But sine and cosine are defined to y/r and x/r respectively.

I'm not sure I understand your statement here. Can you clarify?