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Beliebt Trigonometrie >

sin^2(θ)= 1/9

Lösung

sin^{2} (θ) = \frac{1}{9}

Lösung

θ = 0.33983 \dots + 2 πn, θ = π - 0.33983 \dots + 2 πn, θ = - 0.33983 \dots + 2 πn, θ = π + 0.33983 \dots + 2 πn

+1

Grad

θ = 19.47122 \dots^{\circ} + 36 0^{\circ} n, θ = 160.52877 \dots^{\circ} + 36 0^{\circ} n, θ = - 19.47122 \dots^{\circ} + 36 0^{\circ} n, θ = 199.47122 \dots^{\circ} + 36 0^{\circ} n

Schritte zur Lösung

sin^{2} (θ) = \frac{1}{9}

Löse mit Substitution

sin^{2} (θ) = \frac{1}{9}

Angenommen:

sin (θ) = u

u^{2} = \frac{1}{9}

u^{2} = \frac{1}{9} : u = \frac{1}{3}, u = - \frac{1}{3}

u^{2} = \frac{1}{9}

Für

x^{2} = f (a)

sind die Lösungen

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

u = \frac{1}{9}, u = - \frac{1}{9}

\frac{1}{9} = \frac{1}{3}

\frac{1}{9}

Wende Radikal Regel an:

n \frac{a}{b} = \frac{n a}{n b},

angenommen

a \geq 0, b \geq 0

= \frac{1}{9}

9 = 3

9

Faktorisiere die Zahl:

9 = 3^{2}

= 3^{2}

Wende Radikal Regel an:

n a^{n} = a

3^{2} = 3

= 3

= \frac{1}{3}

Wende Regel an

1 = 1

= \frac{1}{3}

- \frac{1}{9} = - \frac{1}{3}

- \frac{1}{9}

Vereinfache

\frac{1}{9} : \frac{1}{3}

\frac{1}{9}

Wende Radikal Regel an:

n \frac{a}{b} = \frac{n a}{n b},

angenommen

a \geq 0, b \geq 0

= \frac{1}{9}

9 = 3

9

Faktorisiere die Zahl:

9 = 3^{2}

= 3^{2}

Wende Radikal Regel an:

n a^{n} = a

3^{2} = 3

= 3

= \frac{1}{3}

= - \frac{1}{3}

Wende Regel an

1 = 1

= - \frac{1}{3}

u = \frac{1}{3}, u = - \frac{1}{3}

Setze in

u = sin (θ)

ein

sin (θ) = \frac{1}{3}, sin (θ) = - \frac{1}{3}

sin (θ) = \frac{1}{3}, sin (θ) = - \frac{1}{3}

sin (θ) = \frac{1}{3} : θ = arcsin (\frac{1}{3}) + 2 πn, θ = π - arcsin (\frac{1}{3}) + 2 πn

sin (θ) = \frac{1}{3}

Wende die Eigenschaften der Trigonometrie an

sin (θ) = \frac{1}{3}

Allgemeine Lösung für

sin (θ) = \frac{1}{3}

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

θ = arcsin (\frac{1}{3}) + 2 πn, θ = π - arcsin (\frac{1}{3}) + 2 πn

θ = arcsin (\frac{1}{3}) + 2 πn, θ = π - arcsin (\frac{1}{3}) + 2 πn

sin (θ) = - \frac{1}{3} : θ = arcsin (- \frac{1}{3}) + 2 πn, θ = π + arcsin (\frac{1}{3}) + 2 πn

sin (θ) = - \frac{1}{3}

Wende die Eigenschaften der Trigonometrie an

sin (θ) = - \frac{1}{3}

Allgemeine Lösung für

sin (θ) = - \frac{1}{3}

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

θ = arcsin (- \frac{1}{3}) + 2 πn, θ = π + arcsin (\frac{1}{3}) + 2 πn

θ = arcsin (- \frac{1}{3}) + 2 πn, θ = π + arcsin (\frac{1}{3}) + 2 πn

Kombiniere alle Lösungen

θ = arcsin (\frac{1}{3}) + 2 πn, θ = π - arcsin (\frac{1}{3}) + 2 πn, θ = arcsin (- \frac{1}{3}) + 2 πn, θ = π + arcsin (\frac{1}{3}) + 2 πn

Zeige Lösungen in Dezimalform

θ = 0.33983 \dots + 2 πn, θ = π - 0.33983 \dots + 2 πn, θ = - 0.33983 \dots + 2 πn, θ = π + 0.33983 \dots + 2 πn

Graph

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