Änderungen von Dokument Lösung x-Achse

Zuletzt geändert von Holger Engels am 2025/10/09 09:30

Von Version 7.1
bearbeitet von akukin
am 2025/08/29 18:55
Änderungskommentar: Es gibt keinen Kommentar für diese Version
Auf Version 17.2
bearbeitet von Holger Engels
am 2025/10/09 09:30
Änderungskommentar: Es gibt keinen Kommentar für diese Version

Zusammenfassung

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1 -XWiki.akukin
1 +XWiki.holgerengels
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1 1  (%class=abc%)
2 -1. (((Die Periodenlänge der Funktion {{formula}}f(x) = \sin(2(x-2)){{/formula}} ist gegben durch {{formula}}p=\frac{2\pi}{b}=\frac{2\pi}{2}=\pi{{/formula}}.
3 -Zudem ist die Sinusfunktion ist um 2 Einheiten nach rechts verschoben.
2 +1. (((__Mögliche Vorgehensweise:__
3 +Die Periodenlänge der Funktion {{formula}}f(x) = \sin(2(x-\frac{\pi}{2})){{/formula}} ist gegben durch {{formula}}p=\frac{2\pi}{b}=\frac{2\pi}{2}=\pi{{/formula}}.
4 +Zudem ist die Sinusfunktion ist um {{formula}}\frac{\pi}{2}{{/formula}} Einheiten nach rechts verschoben.
4 4  
5 -Um die markanten Punkte (Hoch-, Tief- und x-Achsenschnittpunkte) leicht einzeichnen zu können, wäre es sinnvoll, bei {{formula}}x=2{{/formula}} zu beginnen und die x-Achse von dort aus in Schritten von {{formula}}\frac{\pi}{4}{{/formula}} (ein viertel der Periode) zu beschriften. Als Maßstab kann man dabei pro Schritt einen cm nehmen, d.h. {{formula}}1cm\equiv\frac{\pi}{4}{{/formula}}. Die Verschiebung von 2 würde demnach {{formula}}2:\frac{\pi}{4}\approx 2,55{{/formula}} Einheiten entsprechen.
6 +Um mindestens eine Periode mit den markanten Punkten (Hoch-, Tief- und x-Achsenschnittpunkte) leicht einzeichnen zu können, muss die x-Achse mindestens bis {{formula}}\frac{\pi}{2}+\pi=\frac{3}{2}\pi{{/formula}} reichen und sollte mit {{formula}}\frac{\pi}{4}{{/formula}}- Schritten beschriftet sein.
7 +[[image:sinus.png||width="350" style="display:block;margin-left:auto;margin-right:auto"]]
6 6  )))
7 7  1. (((Die Periodenlänge der Funktion {{formula}}g(x) = \cos(\pi(x-2)){{/formula}} ist gegben durch {{formula}}p=\frac{2\pi}{b}=\frac{2\pi}{\pi}=2{{/formula}}.
8 8  
sinus.ggb
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1 +XWiki.holgerengels
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sinus.svg
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