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Beliebt Trigonometrie >

cos^2(x)=0.25

Lösung

cos^{2} (x) = 0.25

Lösung

x = 1.04719 \dots + 2 πn, x = 2 π - 1.04719 \dots + 2 πn, x = 2.09439 \dots + 2 πn, x = - 2.09439 \dots + 2 πn

+1

Grad

x = 6 0^{\circ} + 36 0^{\circ} n, x = 30 0^{\circ} + 36 0^{\circ} n, x = 12 0^{\circ} + 36 0^{\circ} n, x = - 12 0^{\circ} + 36 0^{\circ} n

Schritte zur Lösung

cos^{2} (x) = 0.25

Löse mit Substitution

cos^{2} (x) = 0.25

Angenommen:

cos (x) = u

u^{2} = 0.25

u^{2} = 0.25 : u = 0.25, u = - 0.25

u^{2} = 0.25

Für

x^{2} = f (a)

sind die Lösungen

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

u = 0.25, u = - 0.25

Setze in

u = cos (x)

ein

cos (x) = 0.25, cos (x) = - 0.25

cos (x) = 0.25, cos (x) = - 0.25

cos (x) = 0.25 : x = arccos (0.25) + 2 πn, x = 2 π - arccos (0.25) + 2 πn

cos (x) = 0.25

Wende die Eigenschaften der Trigonometrie an

cos (x) = 0.25

Allgemeine Lösung für

cos (x) = 0.25

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

x = arccos (0.25) + 2 πn, x = 2 π - arccos (0.25) + 2 πn

x = arccos (0.25) + 2 πn, x = 2 π - arccos (0.25) + 2 πn

cos (x) = - 0.25 : x = arccos (- 0.25) + 2 πn, x = - arccos (- 0.25) + 2 πn

cos (x) = - 0.25

Wende die Eigenschaften der Trigonometrie an

cos (x) = - 0.25

Allgemeine Lösung für

cos (x) = - 0.25

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

x = arccos (- 0.25) + 2 πn, x = - arccos (- 0.25) + 2 πn

x = arccos (- 0.25) + 2 πn, x = - arccos (- 0.25) + 2 πn

Kombiniere alle Lösungen

x = arccos (0.25) + 2 πn, x = 2 π - arccos (0.25) + 2 πn, x = arccos (- 0.25) + 2 πn, x = - arccos (- 0.25) + 2 πn

Zeige Lösungen in Dezimalform

x = 1.04719 \dots + 2 πn, x = 2 π - 1.04719 \dots + 2 πn, x = 2.09439 \dots + 2 πn, x = - 2.09439 \dots + 2 πn

Graph

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