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Beliebt Trigonometrie >

cos^2(a)= 1/5

Lösung

cos^{2} (a) = \frac{1}{5}

Lösung

a = 1.10714 \dots + 2 πn, a = 2 π - 1.10714 \dots + 2 πn, a = 2.03444 \dots + 2 πn, a = - 2.03444 \dots + 2 πn

+1

Grad

a = 63.43494 \dots^{\circ} + 36 0^{\circ} n, a = 296.56505 \dots^{\circ} + 36 0^{\circ} n, a = 116.56505 \dots^{\circ} + 36 0^{\circ} n, a = - 116.56505 \dots^{\circ} + 36 0^{\circ} n

Schritte zur Lösung

cos^{2} (a) = \frac{1}{5}

Löse mit Substitution

cos^{2} (a) = \frac{1}{5}

Angenommen:

cos (a) = u

u^{2} = \frac{1}{5}

u^{2} = \frac{1}{5} : u = \frac{1}{5}, u = - \frac{1}{5}

u^{2} = \frac{1}{5}

Für

x^{2} = f (a)

sind die Lösungen

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

u = \frac{1}{5}, u = - \frac{1}{5}

Setze in

u = cos (a)

ein

cos (a) = \frac{1}{5}, cos (a) = - \frac{1}{5}

cos (a) = \frac{1}{5}, cos (a) = - \frac{1}{5}

cos (a) = \frac{1}{5} : a = arccos (\frac{1}{5}) + 2 πn, a = 2 π - arccos (\frac{1}{5}) + 2 πn

cos (a) = \frac{1}{5}

Wende die Eigenschaften der Trigonometrie an

cos (a) = \frac{1}{5}

Allgemeine Lösung für

cos (a) = \frac{1}{5}

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

a = arccos (\frac{1}{5}) + 2 πn, a = 2 π - arccos (\frac{1}{5}) + 2 πn

a = arccos (\frac{1}{5}) + 2 πn, a = 2 π - arccos (\frac{1}{5}) + 2 πn

cos (a) = - \frac{1}{5} : a = arccos (- \frac{1}{5}) + 2 πn, a = - arccos (- \frac{1}{5}) + 2 πn

cos (a) = - \frac{1}{5}

Wende die Eigenschaften der Trigonometrie an

cos (a) = - \frac{1}{5}

Allgemeine Lösung für

cos (a) = - \frac{1}{5}

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

a = arccos (- \frac{1}{5}) + 2 πn, a = - arccos (- \frac{1}{5}) + 2 πn

a = arccos (- \frac{1}{5}) + 2 πn, a = - arccos (- \frac{1}{5}) + 2 πn

Kombiniere alle Lösungen

a = arccos (\frac{1}{5}) + 2 πn, a = 2 π - arccos (\frac{1}{5}) + 2 πn, a = arccos (- \frac{1}{5}) + 2 πn, a = - arccos (- \frac{1}{5}) + 2 πn

Zeige Lösungen in Dezimalform

a = 1.10714 \dots + 2 πn, a = 2 π - 1.10714 \dots + 2 πn, a = 2.03444 \dots + 2 πn, a = - 2.03444 \dots + 2 πn

Graph

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