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Beliebt Trigonometrie >

sin^2(θ)= 1/4

Lösung

sin^{2} (θ) = \frac{1}{4}

Lösung

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

+1

Grad

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

Schritte zur Lösung

sin^{2} (θ) = \frac{1}{4}

Löse mit Substitution

sin^{2} (θ) = \frac{1}{4}

Angenommen:

sin (θ) = u

u^{2} = \frac{1}{4}

u^{2} = \frac{1}{4} : u = \frac{1}{2}, u = - \frac{1}{2}

u^{2} = \frac{1}{4}

Für

x^{2} = f (a)

sind die Lösungen

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

u = \frac{1}{4}, u = - \frac{1}{4}

\frac{1}{4} = \frac{1}{2}

\frac{1}{4}

Wende Radikal Regel an:

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

angenommen

a \geq 0, b \geq 0

= \frac{1}{4}

4 = 2

4

Faktorisiere die Zahl:

4 = 2^{2}

= 2^{2}

Wende Radikal Regel an:

n a^{n} = a

2^{2} = 2

= 2

= \frac{1}{2}

Wende Regel an

1 = 1

= \frac{1}{2}

- \frac{1}{4} = - \frac{1}{2}

- \frac{1}{4}

Vereinfache

\frac{1}{4} : \frac{1}{2}

\frac{1}{4}

Wende Radikal Regel an:

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

angenommen

a \geq 0, b \geq 0

= \frac{1}{4}

4 = 2

4

Faktorisiere die Zahl:

4 = 2^{2}

= 2^{2}

Wende Radikal Regel an:

n a^{n} = a

2^{2} = 2

= 2

= \frac{1}{2}

= - \frac{1}{2}

Wende Regel an

1 = 1

= - \frac{1}{2}

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

Setze in

u = sin (θ)

ein

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

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

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

sin (θ) = \frac{1}{2}

Allgemeine Lösung für

sin (θ) = \frac{1}{2}

sin (x)

Periodizitätstabelle mit

2 πn

Zyklus:

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

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

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

sin (θ) = - \frac{1}{2}

Allgemeine Lösung für

sin (θ) = - \frac{1}{2}

sin (x)

Periodizitätstabelle mit

2 πn

Zyklus:

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

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

Kombiniere alle Lösungen

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

Graph

Beliebte Beispiele

(tan(θ)+1)(sec(θ)+1)=0

(tan (θ) + 1) (sec (θ) + 1) = 0

2sin(θ)-tan^2(θ)=0

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sin(θ)-sqrt(3)cos(θ)=1

sin (θ) - 3 cos (θ) = 1

cos (a) = \frac{1}{2}

cos^{2} (θ) = \frac{3}{4}