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In diesem Video vermittle ich

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Grundlagen der Trigonometrie.

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Das klingt nach einem komplizierten Thema,

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aber du wirst sehen, es geht nur um

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die Verhältnisse zwischen Seiten von Dreiecken

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"Trig" von Trigonometrie bedeutet

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Dreieck und "metrie" bedeutet

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Maß. Lass mich einfach ein paar Beispiele zeigen.

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Ich denke, das wird alles gut erklären.

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Also, lass mich rechtwinklige Dreiecke zeichnen,

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... So, das ist ein rechtwinkliges Dreieck.

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Ich sage rechtwinkliges Dreieck, weil

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einer der Winkel 90 Grad hat.

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Das rechts hier ist ein rechter Winkel

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Er ist gleich 90 Grad.

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Und wir werden in künftigen Videos noch andere Arten besprechen,

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um die Größe von Winkeln zu zeigen.

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Wir haben also einen 90 Grad Winkel.

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Es ist ein rechter Winkel

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Geben den Seiten hier Längen. 
Diese Seite hier ist vielleicht 3. Die Höhe hier ist 3.

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Die Grundlinie des Dreiecks hier könnte 4 sein.

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Und die Hypotenuse von diesem Dreieck ist 5.

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Hypotenusen gibt es nur in rechtwinkligen Dreiecken.

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Sie ist die Seite gegenüber dem rechten Winkel
und sie ist die längste Seite eines rechtwinkligen Dreiecks.

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Das hier ist die Hypotenuse.

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Das hast du vielleicht in Geometrie schon gelernt.

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Und wir können nachweisen, dass dieses rechwinklige Dreieck stimmt.

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Wir kennen den Pythagoräischen Lehrsatz,

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dass 3 zum Quadrat und 4 zum Quadrat der Länge der längsten Seite entsprechen müssen;

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die Länge der Hypotenuse zum Quadrat ist gleich 5 zum Quadrat

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du kannst also verifizieren, dass es aufgeht

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dass es dem Pythagoräischen Lehrsatz entspricht.

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Nachdem das erledigt ist,
lernen wir ein Bisschen Trigonometrie.

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Die zentralen Funktionen der Trigonometrie,

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wir werden etwas besser lernen, was diese Funktionen bedeuten.

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Es gibt den Sinus, die Sinusfunktion

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Es gibt die Kosinusfunktion, und es gibt die Tangensfunktion.

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Und du schreibst sin, cos und tan als Kurzform

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Das ist eine Gedächtnisstütze hier,

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die helfen soll, sich die Definitionen dieser Funktionen zu merken,

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aber ich werde etwas hinschreiben, nämlich 
"soh cah toa",

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du wirst staunen, wie weit diese Gedankenstütze dich in die Trigonometrie führen wird.

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Wir haben also "soh cah toa", 
und was sagt es uns?

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