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## Basic Integral without Basic Concept

 Quote by dimension10 I think this is not possible. Maybe your friend considers $$\sin\theta=\frac{{e}^{i\theta}-{e}^{-i\theta}}{2i}$$ $$\cos\theta=\frac{{e}^{i\theta}+{e}^{-i\theta}}{2}$$ 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?