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Änderungen von Dokument Lösung Funktionswert bekannt

Zuletzt geändert von Holger Engels am 2025/10/07 05:44
Von Version 4.1
bearbeitet von Holger Engels
am 2025/10/02 21:47
Änderungskommentar: Neues Bild Standard Sinus.png hochladen
Auf Version 5.1
bearbeitet von Holger Engels
am 2025/10/06 06:52
Änderungskommentar: Neues Bild Skizze.svg hochladen

Zusammenfassung

Details

Seiteneigenschaften
Inhalt
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1 -Zwei Wege führen zum Ziel ..
2 -
3 3  **Rückführung auf den Standard Sinus**
4 4  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.
5 5  
6 6  [[image:Standard Sinus.png]]
7 7  
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
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.
9 9  
8 +Von hier aus führen zwei Wege zum Ziel ..
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 +
10 10  {{formula}}f(x)=\sin(\frac{1}{6}\pi(x-1)){{/formula}}
11 11  
12 12  **Skizze**
Skizze.svg
Größe
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1 -39.4 KB
1 +45.4 KB
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