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Beliebt Trigonometrie >

sin(x)=(-1}{\frac{sqrt(5))/2}

Lösung

sin (x) = \frac{- 1}{\frac{5}{2}}

Lösung

x = - 1.10714 \dots + 2 πn, x = π + 1.10714 \dots + 2 πn

+1

Radianten

x = - 1.10714 \dots + 6.28318 \dots n, x = π + 1.10714 \dots + 6.28318 \dots n

Schritte zur Lösung

sin (x) = \frac{- 1}{\frac{5}{2}}

Vereinfache

\frac{- 1}{\frac{5}{2}} : - \frac{2 5}{5}

\frac{- 1}{\frac{5}{2}}

Wende Bruchregel an:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{1}{\frac{5}{2}}

Wende Bruchregel an:

\frac{1}{\frac{b}{c}} = \frac{c}{b}

\frac{1}{\frac{5}{2}} = \frac{2}{5}

= - \frac{2}{5}

Rationalisiere

- \frac{2}{5} : - \frac{2 5}{5}

- \frac{2}{5}

Multipliziere mit dem Konjugat

\frac{5}{5}

= - \frac{2 5}{5 5}

55 = 5

55

Wende Radikal Regel an:

a a = a

55 = 5

= 5

= - \frac{2 5}{5}

= - \frac{2 5}{5}

sin (x) = - \frac{2 5}{5}

Wende die Eigenschaften der Trigonometrie an

sin (x) = - \frac{2 5}{5}

Allgemeine Lösung für

sin (x) = - \frac{2 5}{5}

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

x = arcsin (- \frac{2 5}{5}) + 2 πn, x = π + arcsin (\frac{2 5}{5}) + 2 πn

x = arcsin (- \frac{2 5}{5}) + 2 πn, x = π + arcsin (\frac{2 5}{5}) + 2 πn

Zeige Lösungen in Dezimalform

x = - 1.10714 \dots + 2 πn, x = π + 1.10714 \dots + 2 πn

Graph

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