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Beliebt Trigonometrie >

|sin(x)|= 1/2

Lösung

∣ sin (x) ∣ = \frac{1}{2}

Lösung

x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn, x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

+1

Grad

x = 21 0^{\circ} + 36 0^{\circ} n, x = 33 0^{\circ} + 36 0^{\circ} n, x = 3 0^{\circ} + 36 0^{\circ} n, x = 15 0^{\circ} + 36 0^{\circ} n

Schritte zur Lösung

∣ sin (x) ∣ = \frac{1}{2}

Löse mit Substitution

∣ sin (x) ∣ = \frac{1}{2}

Angenommen:

sin (x) = u

∣ u ∣ = \frac{1}{2}

∣ u ∣ = \frac{1}{2} : u = - \frac{1}{2} or u = \frac{1}{2}

∣ u ∣ = \frac{1}{2}

Wende Absoluteregel an: Wenn

∣ u ∣ = a, a > 0

dann

u = a

or

u = - a

u = - \frac{1}{2} or u = \frac{1}{2}

Setze in

u = sin (x)

ein

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

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

sin (x) = - \frac{1}{2} : x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

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

Allgemeine Lösung für

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

sin (x)

Periodizitätstabelle mit

2 πn

Zyklus:

x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

sin (x) = \frac{1}{2} : x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

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

Allgemeine Lösung für

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

sin (x)

Periodizitätstabelle mit

2 πn

Zyklus:

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Kombiniere alle Lösungen

x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn, x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Graph

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