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Beliebt Trigonometrie >

csc^2(t)=3

Lösung

csc^{2} (t) = 3

Lösung

t = 0.61547 \dots + 2 πn, t = π - 0.61547 \dots + 2 πn, t = - 0.61547 \dots + 2 πn, t = π + 0.61547 \dots + 2 πn

+1

Grad

t = 35.26438 \dots^{\circ} + 36 0^{\circ} n, t = 144.73561 \dots^{\circ} + 36 0^{\circ} n, t = - 35.26438 \dots^{\circ} + 36 0^{\circ} n, t = 215.26438 \dots^{\circ} + 36 0^{\circ} n

Schritte zur Lösung

csc^{2} (t) = 3

Löse mit Substitution

csc^{2} (t) = 3

Angenommen:

csc (t) = u

u^{2} = 3

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

u^{2} = 3

Für

x^{2} = f (a)

sind die Lösungen

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

u = 3, u = - 3

Setze in

u = csc (t)

ein

csc (t) = 3, csc (t) = - 3

csc (t) = 3, csc (t) = - 3

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

csc (t) = 3

Wende die Eigenschaften der Trigonometrie an

csc (t) = 3

Allgemeine Lösung für

csc (t) = 3

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

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

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

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

csc (t) = - 3

Wende die Eigenschaften der Trigonometrie an

csc (t) = - 3

Allgemeine Lösung für

csc (t) = - 3

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

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

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

Kombiniere alle Lösungen

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

Zeige Lösungen in Dezimalform

t = 0.61547 \dots + 2 πn, t = π - 0.61547 \dots + 2 πn, t = - 0.61547 \dots + 2 πn, t = π + 0.61547 \dots + 2 πn

Graph

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