Corollary: All Zeros of Cosine and Sine

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

The zeros the real sine $\sin(x)=0$ are exactly the numbers $x=k\pi,$ and of the real cosine $\cos(x)=0$ are exactly the numbers $x=\left(k+\frac 12\right)\pi,$ in which $k\in\mathbb Z$ denotes an integer and $\pi$ denotes the $\pi$ constant. Formally,

$$\sin(x)=0\Longleftrightarrow x=k\pi,\quad k\in\mathbb Z.$$ $$\cos(x)=0\Longleftrightarrow x=\left(k+\frac 12\right)\pi,\quad k\in\mathbb Z.$$

Proofs: 1

Proofs: 1

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