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5Frage: Berechne \(\cos 150^\circ\).
Lösung: Wir wissen, dass \(\cos(180^\circ - \theta) = -\cos \theta\). Somit ist \(\cos 150^\circ = \cos(180^\circ - 30^\circ) = -\cos 30^\circ\). Unter Verwendung des bekannten Wertes \(\cos 30^\circ = \frac{\sqrt{3}}{2}\), finden wir \(\cos 150^\circ = -\frac{\sqrt{3}}{2}\). Daher ist die Antwort \(\boxed{-\frac{\sqrt{3}}{2}}\).
Frage: Ein gleichseitiges Dreieck hat einen Umfang von 24 cm. Wenn jede Seite des Dreiecks um 2 cm vergrößert wird, um wie viele Quadratzentimeter erhöht sich die Fläche?