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Beliebt Trigonometrie >

sin^{22}(x)= 1/2

Lösung

sin^{22} (x) = \frac{1}{2}

Lösung

x = 1.32108 \dots + 2 πn, x = π - 1.32108 \dots + 2 πn, x = - 1.32108 \dots + 2 πn, x = π + 1.32108 \dots + 2 πn

+1

Grad

x = 75.69275 \dots^{\circ} + 36 0^{\circ} n, x = 104.30724 \dots^{\circ} + 36 0^{\circ} n, x = - 75.69275 \dots^{\circ} + 36 0^{\circ} n, x = 255.69275 \dots^{\circ} + 36 0^{\circ} n

Schritte zur Lösung

sin^{22} (x) = \frac{1}{2}

Löse mit Substitution

sin^{22} (x) = \frac{1}{2}

Angenommen:

sin (x) = u

u^{22} = \frac{1}{2}

u^{22} = \frac{1}{2} : u = 22 \frac{1}{2}, u = - 22 \frac{1}{2}

u^{22} = \frac{1}{2}

Für

x^{n} = f (a)

, n ist gerade, die Lösungen sind

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

u = 22 \frac{1}{2}, u = - 22 \frac{1}{2}

Setze in

u = sin (x)

ein

sin (x) = 22 \frac{1}{2}, sin (x) = - 22 \frac{1}{2}

sin (x) = 22 \frac{1}{2}, sin (x) = - 22 \frac{1}{2}

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

sin (x) = 22 \frac{1}{2}

Wende die Eigenschaften der Trigonometrie an

sin (x) = 22 \frac{1}{2}

Allgemeine Lösung für

sin (x) = 22 \frac{1}{2}

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

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

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

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

sin (x) = - 22 \frac{1}{2}

Wende die Eigenschaften der Trigonometrie an

sin (x) = - 22 \frac{1}{2}

Allgemeine Lösung für

sin (x) = - 22 \frac{1}{2}

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

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

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

Kombiniere alle Lösungen

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

Zeige Lösungen in Dezimalform

x = 1.32108 \dots + 2 πn, x = π - 1.32108 \dots + 2 πn, x = - 1.32108 \dots + 2 πn, x = π + 1.32108 \dots + 2 πn

Graph

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