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Beliebt Trigonometrie >

sin^2(x)+0.49=1

Lösung

sin^{2} (x) + 0.49 = 1

Lösung

x = 0.79539 \dots + 2 πn, x = π - 0.79539 \dots + 2 πn, x = - 0.79539 \dots + 2 πn, x = π + 0.79539 \dots + 2 πn

+1

Grad

x = 45.57299 \dots^{\circ} + 36 0^{\circ} n, x = 134.42700 \dots^{\circ} + 36 0^{\circ} n, x = - 45.57299 \dots^{\circ} + 36 0^{\circ} n, x = 225.57299 \dots^{\circ} + 36 0^{\circ} n

Schritte zur Lösung

sin^{2} (x) + 0.49 = 1

Löse mit Substitution

sin^{2} (x) + 0.49 = 1

Angenommen:

sin (x) = u

u^{2} + 0.49 = 1

u^{2} + 0.49 = 1 : u = 0.51, u = - 0.51

u^{2} + 0.49 = 1

Verschiebe

0.49

auf die rechte Seite

u^{2} + 0.49 = 1

Subtrahiere

0.49

von beiden Seiten

u^{2} + 0.49 - 0.49 = 1 - 0.49

Vereinfache

u^{2} = 0.51

u^{2} = 0.51

Für

x^{2} = f (a)

sind die Lösungen

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

u = 0.51, u = - 0.51

Setze in

u = sin (x)

ein

sin (x) = 0.51, sin (x) = - 0.51

sin (x) = 0.51, sin (x) = - 0.51

sin (x) = 0.51 : x = arcsin (0.51) + 2 πn, x = π - arcsin (0.51) + 2 πn

sin (x) = 0.51

Wende die Eigenschaften der Trigonometrie an

sin (x) = 0.51

Allgemeine Lösung für

sin (x) = 0.51

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

x = arcsin (0.51) + 2 πn, x = π - arcsin (0.51) + 2 πn

x = arcsin (0.51) + 2 πn, x = π - arcsin (0.51) + 2 πn

sin (x) = - 0.51 : x = arcsin (- 0.51) + 2 πn, x = π + arcsin (0.51) + 2 πn

sin (x) = - 0.51

Wende die Eigenschaften der Trigonometrie an

sin (x) = - 0.51

Allgemeine Lösung für

sin (x) = - 0.51

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

x = arcsin (- 0.51) + 2 πn, x = π + arcsin (0.51) + 2 πn

x = arcsin (- 0.51) + 2 πn, x = π + arcsin (0.51) + 2 πn

Kombiniere alle Lösungen

x = arcsin (0.51) + 2 πn, x = π - arcsin (0.51) + 2 πn, x = arcsin (- 0.51) + 2 πn, x = π + arcsin (0.51) + 2 πn

Zeige Lösungen in Dezimalform

x = 0.79539 \dots + 2 πn, x = π - 0.79539 \dots + 2 πn, x = - 0.79539 \dots + 2 πn, x = π + 0.79539 \dots + 2 πn

Graph

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