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Beliebt Trigonometrie >

sin^2(x)=0.5

Lösung

sin^{2} (x) = 0.5

Lösung

x = 0.78539 \dots + 2 πn, x = π - 0.78539 \dots + 2 πn, x = - 0.78539 \dots + 2 πn, x = π + 0.78539 \dots + 2 πn

+1

Grad

x = 4 5^{\circ} + 36 0^{\circ} n, x = 13 5^{\circ} + 36 0^{\circ} n, x = - 4 5^{\circ} + 36 0^{\circ} n, x = 22 5^{\circ} + 36 0^{\circ} n

Schritte zur Lösung

sin^{2} (x) = 0.5

Löse mit Substitution

sin^{2} (x) = 0.5

Angenommen:

sin (x) = u

u^{2} = 0.5

u^{2} = 0.5 : u = 0.5, u = - 0.5

u^{2} = 0.5

Für

x^{2} = f (a)

sind die Lösungen

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

u = 0.5, u = - 0.5

Setze in

u = sin (x)

ein

sin (x) = 0.5, sin (x) = - 0.5

sin (x) = 0.5, sin (x) = - 0.5

sin (x) = 0.5 : x = arcsin (0.5) + 2 πn, x = π - arcsin (0.5) + 2 πn

sin (x) = 0.5

Wende die Eigenschaften der Trigonometrie an

sin (x) = 0.5

Allgemeine Lösung für

sin (x) = 0.5

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

x = arcsin (0.5) + 2 πn, x = π - arcsin (0.5) + 2 πn

x = arcsin (0.5) + 2 πn, x = π - arcsin (0.5) + 2 πn

sin (x) = - 0.5 : x = arcsin (- 0.5) + 2 πn, x = π + arcsin (0.5) + 2 πn

sin (x) = - 0.5

Wende die Eigenschaften der Trigonometrie an

sin (x) = - 0.5

Allgemeine Lösung für

sin (x) = - 0.5

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

x = arcsin (- 0.5) + 2 πn, x = π + arcsin (0.5) + 2 πn

x = arcsin (- 0.5) + 2 πn, x = π + arcsin (0.5) + 2 πn

Kombiniere alle Lösungen

x = arcsin (0.5) + 2 πn, x = π - arcsin (0.5) + 2 πn, x = arcsin (- 0.5) + 2 πn, x = π + arcsin (0.5) + 2 πn

Zeige Lösungen in Dezimalform

x = 0.78539 \dots + 2 πn, x = π - 0.78539 \dots + 2 πn, x = - 0.78539 \dots + 2 πn, x = π + 0.78539 \dots + 2 πn

Graph

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