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Beliebt Trigonometrie >

sin^2(x)+cos(2x)=0

Lösung

sin^{2} (x) + cos (2 x) = 0

Lösung

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

+1

Grad

x = 9 0^{\circ} + 36 0^{\circ} n, x = 27 0^{\circ} + 36 0^{\circ} n

Schritte zur Lösung

sin^{2} (x) + cos (2 x) = 0

Umschreiben mit Hilfe von Trigonometrie-Identitäten

cos (2 x) + sin^{2} (x)

Verwende die Doppelwinkelidentität:

cos^{2} (x) - sin^{2} (x) = cos (2 x)

- sin^{2} (x) = cos (2 x) - cos^{2} (x)

= cos (2 x) - (cos (2 x) - cos^{2} (x))

Vereinfache

cos (2 x) - (cos (2 x) - cos^{2} (x)) : cos^{2} (x)

cos (2 x) - (cos (2 x) - cos^{2} (x))

- (cos (2 x) - cos^{2} (x)) : - cos (2 x) + cos^{2} (x)

- (cos (2 x) - cos^{2} (x))

Setze Klammern

= - (cos (2 x)) - (- cos^{2} (x))

Wende Minus-Plus Regeln an

- (- a) = a, - (a) = - a

= - cos (2 x) + cos^{2} (x)

= cos (2 x) - cos (2 x) + cos^{2} (x)

Addiere gleiche Elemente:

cos (2 x) - cos (2 x) = 0

= cos^{2} (x)

= cos^{2} (x)

cos^{2} (x) = 0

Wende Regel an

x^{n} = 0 \Rightarrow x = 0

cos (x) = 0

Allgemeine Lösung für

cos (x) = 0

cos (x)

Periodizitätstabelle mit

2 πn

Zyklus:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

Graph

Beliebte Beispiele

sin(x)=cos(x+pi/2)

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