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Beliebt Trigonometrie >

(d^2-4)=cos^2(x)

Lösung

(d^{2} - 4) = cos^{2} (x)

Lösung

x = arccos (d^{2} - 4) + 2 πn, x = - arccos (d^{2} - 4) + 2 πn, x = arccos (- d^{2} - 4) + 2 πn, x = - arccos (- d^{2} - 4) + 2 πn

Schritte zur Lösung

(d^{2} - 4) = cos^{2} (x)

Tausche die Seiten

cos^{2} (x) = d^{2} - 4

Löse mit Substitution

cos^{2} (x) = d^{2} - 4

Angenommen:

cos (x) = u

u^{2} = d^{2} - 4

u^{2} = d^{2} - 4 : u = d^{2} - 4, u = - d^{2} - 4

u^{2} = d^{2} - 4

Für

x^{2} = f (a)

sind die Lösungen

x = f (a), - f (a)

u = d^{2} - 4, u = - d^{2} - 4

Setze in

u = cos (x)

ein

cos (x) = d^{2} - 4, cos (x) = - d^{2} - 4

cos (x) = d^{2} - 4, cos (x) = - d^{2} - 4

cos (x) = d^{2} - 4 : x = arccos (d^{2} - 4) + 2 πn, x = - arccos (d^{2} - 4) + 2 πn

cos (x) = d^{2} - 4

Wende die Eigenschaften der Trigonometrie an

cos (x) = d^{2} - 4

Allgemeine Lösung für

cos (x) = d^{2} - 4

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = - arccos (a) + 2 πn

x = arccos (d^{2} - 4) + 2 πn, x = - arccos (d^{2} - 4) + 2 πn

x = arccos (d^{2} - 4) + 2 πn, x = - arccos (d^{2} - 4) + 2 πn

cos (x) = - d^{2} - 4 : x = arccos (- d^{2} - 4) + 2 πn, x = - arccos (- d^{2} - 4) + 2 πn

cos (x) = - d^{2} - 4

Wende die Eigenschaften der Trigonometrie an

cos (x) = - d^{2} - 4

Allgemeine Lösung für

cos (x) = - d^{2} - 4

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = - arccos (a) + 2 πn

x = arccos (- d^{2} - 4) + 2 πn, x = - arccos (- d^{2} - 4) + 2 πn

x = arccos (- d^{2} - 4) + 2 πn, x = - arccos (- d^{2} - 4) + 2 πn

Kombiniere alle Lösungen

x = arccos (d^{2} - 4) + 2 πn, x = - arccos (d^{2} - 4) + 2 πn, x = arccos (- d^{2} - 4) + 2 πn, x = - arccos (- d^{2} - 4) + 2 πn

Graph

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