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Corollary: Representing Real Sine by Complex Exponential Function

(related to Definition: Sine of a Real Variable)

The sine of a real variable \(\sin:\mathbb R\to \mathbb R\) can be represented by the exponential function of a complex variable by the following formula:

\[\sin(x)=\frac 1{2i}(\exp(ix)-\exp(-ix)).\]

An alternative notation for this formula is

\[\sin(x)=\frac 1{2i}(e^{ix}-e^{-ix}).\]

Table of Contents

Proofs: 1

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Proofs: 1 2

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References

Bibliography

1. Forster Otto: "Analysis 1, Differential- und Integralrechnung einer Veränderlichen", Vieweg Studium, 1983