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Beliebt Trigonometrie >

sin^{22}(x)= 1/4

Lösung

sin^{22} (x) = \frac{1}{4}

Lösung

x = 1.21951 \dots + 2 πn, x = π - 1.21951 \dots + 2 πn, x = - 1.21951 \dots + 2 πn, x = π + 1.21951 \dots + 2 πn

+1

Grad

x = 69.87278 \dots^{\circ} + 36 0^{\circ} n, x = 110.12721 \dots^{\circ} + 36 0^{\circ} n, x = - 69.87278 \dots^{\circ} + 36 0^{\circ} n, x = 249.87278 \dots^{\circ} + 36 0^{\circ} n

Schritte zur Lösung

sin^{22} (x) = \frac{1}{4}

Löse mit Substitution

sin^{22} (x) = \frac{1}{4}

Angenommen:

sin (x) = u

u^{22} = \frac{1}{4}

u^{22} = \frac{1}{4} : u = 22 \frac{1}{4}, u = - 22 \frac{1}{4}

u^{22} = \frac{1}{4}

Für

x^{n} = f (a)

, n ist gerade, die Lösungen sind

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

u = 22 \frac{1}{4}, u = - 22 \frac{1}{4}

Setze in

u = sin (x)

ein

sin (x) = 22 \frac{1}{4}, sin (x) = - 22 \frac{1}{4}

sin (x) = 22 \frac{1}{4}, sin (x) = - 22 \frac{1}{4}

sin (x) = 22 \frac{1}{4} : x = arcsin (22 \frac{1}{4}) + 2 πn, x = π - arcsin (22 \frac{1}{4}) + 2 πn

sin (x) = 22 \frac{1}{4}

Wende die Eigenschaften der Trigonometrie an

sin (x) = 22 \frac{1}{4}

Allgemeine Lösung für

sin (x) = 22 \frac{1}{4}

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

x = arcsin (22 \frac{1}{4}) + 2 πn, x = π - arcsin (22 \frac{1}{4}) + 2 πn

x = arcsin (22 \frac{1}{4}) + 2 πn, x = π - arcsin (22 \frac{1}{4}) + 2 πn

sin (x) = - 22 \frac{1}{4} : x = arcsin (- 22 \frac{1}{4}) + 2 πn, x = π + arcsin (22 \frac{1}{4}) + 2 πn

sin (x) = - 22 \frac{1}{4}

Wende die Eigenschaften der Trigonometrie an

sin (x) = - 22 \frac{1}{4}

Allgemeine Lösung für

sin (x) = - 22 \frac{1}{4}

sin (x) = - a \Rightarrow x = arcsin (- a) + 2 πn, x = π + arcsin (a) + 2 πn

x = arcsin (- 22 \frac{1}{4}) + 2 πn, x = π + arcsin (22 \frac{1}{4}) + 2 πn

x = arcsin (- 22 \frac{1}{4}) + 2 πn, x = π + arcsin (22 \frac{1}{4}) + 2 πn

Kombiniere alle Lösungen

x = arcsin (22 \frac{1}{4}) + 2 πn, x = π - arcsin (22 \frac{1}{4}) + 2 πn, x = arcsin (- 22 \frac{1}{4}) + 2 πn, x = π + arcsin (22 \frac{1}{4}) + 2 πn

Zeige Lösungen in Dezimalform

x = 1.21951 \dots + 2 πn, x = π - 1.21951 \dots + 2 πn, x = - 1.21951 \dots + 2 πn, x = π + 1.21951 \dots + 2 πn

Graph

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