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Corollary: Negative Cosine and Sine vs Shifting the Argument

(related to Proposition: Special Values for Real Sine, Real Cosine and Complex Exponential Function)

For all real numbers $x\in\mathbb R$, we can shift the argument of the real cosine and real sine by the $\pi$ constant to get the negative values of these functions, formally $$\cos(x+\pi)=-\cos(x),\quad\quad\sin(x+\pi)=-\sin(x).$$

Table of Contents

Proofs: 1

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References

Bibliography

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