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Beliebt Trigonometrie >

cos(x)=sqrt(9/10)

Lösung

cos (x) = \frac{9}{10}

Lösung

x = 0.32175 \dots + 2 πn, x = 2 π - 0.32175 \dots + 2 πn

+1

Radianten

x = 0.32175 \dots + 6.28318 \dots n, x = 5.96143 \dots + 6.28318 \dots n

Schritte zur Lösung

cos (x) = \frac{9}{10}

Vereinfache

\frac{9}{10} : \frac{3 10}{10}

\frac{9}{10}

Wende Radikal Regel an:

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

angenommen

a \geq 0, b \geq 0

= \frac{9}{10}

9 = 3

9

Faktorisiere die Zahl:

9 = 3^{2}

= 3^{2}

Wende Radikal Regel an:

n a^{n} = a

3^{2} = 3

= 3

= \frac{3}{10}

Rationalisiere

\frac{3}{10} : \frac{3 10}{10}

\frac{3}{10}

Multipliziere mit dem Konjugat

\frac{10}{10}

= \frac{3 10}{10 10}

1010 = 10

1010

Wende Radikal Regel an:

a a = a

1010 = 10

= 10

= \frac{3 10}{10}

= \frac{3 10}{10}

cos (x) = \frac{3 10}{10}

Wende die Eigenschaften der Trigonometrie an

cos (x) = \frac{3 10}{10}

Allgemeine Lösung für

cos (x) = \frac{3 10}{10}

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = 2 π - arccos (a) + 2 πn

x = arccos (\frac{3 10}{10}) + 2 πn, x = 2 π - arccos (\frac{3 10}{10}) + 2 πn

x = arccos (\frac{3 10}{10}) + 2 πn, x = 2 π - arccos (\frac{3 10}{10}) + 2 πn

Zeige Lösungen in Dezimalform

x = 0.32175 \dots + 2 πn, x = 2 π - 0.32175 \dots + 2 πn

Graph

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