Die meisten von uns sollten [math]sin(\alpha)[/math] schon in der Mittelstufe als eine Winkelbeziehung im rechtwinkligen Dreieck kennengelernt haben, als "[color=#980000]Sinus Alpha ist gleich Gegenkathete durch Hypothenuse[/color]":[br][img]https://www.schoepe-online.de/BGPhysik12-2/BGPhysik12-2_files/1.1_Schwingungen_-_Einf%C3%BChrung/1.1_Mathematische_Eigenschaften_der_Sinusfunktion/pasted_image003.png[/img][br][math]\boxed{\Large{\sin(\alpha)=\frac ac}}[/math][br][br]Eine Funktionsgleichung [math]\sin(x)[/math] erhält man, wenn man einen Zeiger in einem Einheitskreis rotieren lässt ([b][url=https://www.geogebra.org/m/ckxkgw7a]siehe hier[/url][/b]).
Die Sinusfunktion hat einige Merkmale, an denen man sie gut erkennen kann:[br][img]data:image/png;base64,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[/img][br][list=1][*]Die Sinusfunktion ist [b][color=#980000]periodisch[/color][/b]. Der blau markierte Teil des oben abgebildeten Funktionsgraphen wiederholt sich unendlich oft in beide Richtungen, also für [math]x\to+\infty[/math] und für [math]x\to-\infty[/math]. Das Intervall, in dem die erste (blaue) Periode der Sinusfunktion liegt, ist [math][0;2\,\pi][/math]. Man sagt auch, die Sinusfunktion hat eine Periodenlänge von [math]2\,\pi[/math]. [br][/*][*]Die [b][color=#980000]Nullstellen[/color][/b] der Sinusfunktion liegen bei einem Vielfachen der Kreiszahl [math]\pi[/math]. Also [math]x_N=z\cdot\pi[/math], wobei z eine beliebige ganze Zahl ist: [math]z\in\mathbb{Z}[/math]. Bei den Nullstellen liegen auch die [b][color=#980000]Wendepunkte[/color][/b] der Funktion: [math]\mathbf W(z\cdot \pi\;\vert\; 0)[/math].[/*][*]Der [b][color=#980000]Hochpunkt[/color][/b] der ersten Periode liegt bei [math]\mathbf{H}(\frac{1}{2}\pi\;|\;1)[/math] . Weil die Sinusfunktion periodisch ist, gibt es jeweils mit einem Abstand von [math]2\pi[/math] nach links und nach rechts auf der Abszisse verschoben unendlich viele weitere Hochpunkte [math]\mathbf{H}(\frac{1}{2}\pi +z\cdot 2\pi\;|\;1)[/math] mit [math]z\in\mathbb{Z}[/math]. Diese haben alle den Funktionswert [math]\sin(\frac{1}{2}\pi)=1[/math]. [br][/*][*]Der [b][color=#980000]Tiefpunkt[/color][/b] der ersten Periode liegt bei [math]\mathbf{T}(\frac{3}{2}\pi\;|\;-1)[/math] . Weil die Sinusfunktion periodisch ist, gibt es jeweils mit einem Abstand von [math]2\pi[/math] nach links und nach rechts auf der Abszisse verschoben unendlich viele weitere Tiefpunkte [math]\mathbf{T}(\frac{3}{2}\pi +z\cdot 2\pi\;|\;1)[/math] mit [math]z\in\mathbb{Z}[/math]. Diese haben alle den Funktionswert [math]\sin(\frac{3}{2}\pi)=-1[/math]. [br][/*][/list]