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Corollary: Representing Real Cosine by Complex Exponential Function

(related to Definition: Cosine of a Real Variable)

The cosine of a real variable $\cos:\mathbb R\to \mathbb R$ can be represented by the exponential function of a complex variable by the following formula:

$$\cos(x)=\frac 12(\exp(ix)+\exp(-ix)).$$

An alternative notation for this formula is

$$\cos(x)=\frac 12(e^{ix}+e^{-ix}).$$

Table of Contents

Proofs: 1

Mentioned in:

Proofs: 1 2

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References

Bibliography

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