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Änderungen von Dokument Lösung Funktionswert bekannt

Zuletzt geändert von Holger Engels am 2025/10/07 05:44
Von Version 6.3
bearbeitet von Holger Engels
am 2025/10/07 05:44
Änderungskommentar: Es gibt keinen Kommentar für diese Version
Auf Version 3.1
bearbeitet von Holger Engels
am 2025/10/02 21:47
Änderungskommentar: Neues Bild Skizze.svg hochladen

Zusammenfassung

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Inhalt
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1 +Zwei Wege führen zum Ziel ..
2 +
1 1  **Rückführung auf den Standard Sinus**
2 2  Wenn man es nicht auswendig weiß, kann man den Taschenrechner zuhilfe nehmen, um zu ermitteln, dass die Standard Sinusfunktion den Wert //0,5// an der Stelle {{formula}}x_1=\frac16\pi{{/formula}} annimmt. Mithilfe einer Skizze der Standard Sinusfunktion findet man die zweite Stelle in der Periode {{formula}}x_2=\frac56\pi{{/formula}}, wo sie wieder diesen Wert annimmt.
3 3  
4 4  [[image:Standard Sinus.png]]
5 5  
6 -Eine gestreckte Sinusfuntktion nimmt demnach die Hälfte ihrer Amplitude bei {{formula}}\frac{1}{12}{{/formula}} und {{formula}}\frac{5}{12}{{/formula}} ihrer Periode an.
8 +Die Standard Sinusfunktion nimmt diesen Wert also bei {{formula}}\frac{1}{12}{{/formula}} und {{formula}}\frac{5}{12}{{/formula}} der Periode an. Der (horizontale) Abstand //6 - 2 = 4// entspricht also {{formula}}\frac{4}{12}{{/formula}} der Periode. Die Periodenlänge beträgt demnach //p = 12//. Der Mittelliniendurchgang ist {{formula}}\frac{1}{12}{{/formula}} links vom ersten Punkt, also an der Stelle //x = 1//. Damit ergibt sich der Funktionsterm
7 7  
8 -Von hier aus führen zwei Wege zum Ziel ..
10 +{{formula}}f(x)=\sin(\frac{1}{6}\pi(x-1)){{/formula}}
9 9  
10 -**Periodenlänge berechnen**
11 -Der (horizontale) Abstand //6 - 2 = 4// entspricht also {{formula}}\frac{4}{12}{{/formula}} der Periode. Die Periodenlänge beträgt demnach //p = 12//. Der Mittelliniendurchgang ist {{formula}}\frac{1}{12}{{/formula}} links vom ersten Punkt, also an der Stelle //x = 1//. Damit ergibt sich der Funktionsterm
12 -
13 -{{formula}}f(x)=2\cdot\sin(\frac{1}{6}\pi(x-1)){{/formula}}
14 -
15 15  **Skizze**
16 16  [[image:Skizze.svg]]
17 -Der Skizze kann man Hochpunkt und Mittelliniendurchgänge entnehmen. Daraus ergeben sich Periodenlänge und horizontale Verschiebung.
14 +Der Skizze kann man die Mittelliniendurchgänge entnehmen. Daraus ergeben sich Periodenlänge und horizontale Verschiebung.
Skizze.ggb
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Skizze.svg
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