Complex Sine Function is Unbounded
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Let $\sin: \C \to \C$ be the complex sine function.
Then $\sin$ is unbounded.
However we have, for instance, by Sine of Zero is Zero:
- $\sin 0 = 0$
and by Sine of 90 Degrees:
- $\sin \dfrac \pi 2 = 1$
Therefore, $\sin$ is clearly not a constant function, a contradiction.