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Beliebt Trigonometrie >

csc^2(x)=9

Lösung

csc^{2} (x) = 9

Lösung

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

+1

Grad

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

Schritte zur Lösung

csc^{2} (x) = 9

Löse mit Substitution

csc^{2} (x) = 9

Angenommen:

csc (x) = u

u^{2} = 9

u^{2} = 9 : u = 3, u = - 3

u^{2} = 9

Für

x^{2} = f (a)

sind die Lösungen

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

u = 9, u = - 9

9 = 3

9

Faktorisiere die Zahl:

9 = 3^{2}

= 3^{2}

Wende Radikal Regel an:

n a^{n} = a

3^{2} = 3

= 3

- 9 = - 3

- 9

9 = 3

9

Faktorisiere die Zahl:

9 = 3^{2}

= 3^{2}

Wende Radikal Regel an:

n a^{n} = a

3^{2} = 3

= 3

= - 3

u = 3, u = - 3

Setze in

u = csc (x)

ein

csc (x) = 3, csc (x) = - 3

csc (x) = 3, csc (x) = - 3

csc (x) = 3 : x = arccsc (3) + 2 πn, x = π - arccsc (3) + 2 πn

csc (x) = 3

Wende die Eigenschaften der Trigonometrie an

csc (x) = 3

Allgemeine Lösung für

csc (x) = 3

csc (x) = a \Rightarrow x = arccsc (a) + 2 πn, x = π - arccsc (a) + 2 πn

x = arccsc (3) + 2 πn, x = π - arccsc (3) + 2 πn

x = arccsc (3) + 2 πn, x = π - arccsc (3) + 2 πn

csc (x) = - 3 : x = arccsc (- 3) + 2 πn, x = π + arccsc (3) + 2 πn

csc (x) = - 3

Wende die Eigenschaften der Trigonometrie an

csc (x) = - 3

Allgemeine Lösung für

csc (x) = - 3

csc (x) = - a \Rightarrow x = arccsc (- a) + 2 πn, x = π + arccsc (a) + 2 πn

x = arccsc (- 3) + 2 πn, x = π + arccsc (3) + 2 πn

x = arccsc (- 3) + 2 πn, x = π + arccsc (3) + 2 πn

Kombiniere alle Lösungen

x = arccsc (3) + 2 πn, x = π - arccsc (3) + 2 πn, x = arccsc (- 3) + 2 πn, x = π + arccsc (3) + 2 πn

Zeige Lösungen in Dezimalform

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

Graph

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