Properties of y = sin x and its graph

$y=\sin x$ : range and zeros

$D(\sin)=\mathbb{R}$ . Range: $E(\sin)=[-1;1]$ , because on the unit circle the y-coordinate always lies in $[-1;1]$ . Zeros: $\sin x=0 \Leftrightarrow x=\pi k,\ k\in\mathbb{Z}$ — points where the motion on the circle crosses the $x$ -axis. Extrema: $\sin x=1$ at $x=\dfrac{\pi}{2}+2\pi k$ , $\sin x=-1$ at $x=-\dfrac{\pi}{2}+2\pi k$ , $k\in\mathbb{Z}$ .

$\sin$ is odd: $\sin(-x)=-\sin x$ ⇒ the graph is symmetric about the origin

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