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Beliebt Trigonometrie >

cos^2(x)= 1/9

Lösung

cos^{2} (x) = \frac{1}{9}

Lösung

x = 1.23095 \dots + 2 πn, x = 2 π - 1.23095 \dots + 2 πn, x = 1.91063 \dots + 2 πn, x = - 1.91063 \dots + 2 πn

+1

Grad

x = 70.52877 \dots^{\circ} + 36 0^{\circ} n, x = 289.47122 \dots^{\circ} + 36 0^{\circ} n, x = 109.47122 \dots^{\circ} + 36 0^{\circ} n, x = - 109.47122 \dots^{\circ} + 36 0^{\circ} n

Schritte zur Lösung

cos^{2} (x) = \frac{1}{9}

Löse mit Substitution

cos^{2} (x) = \frac{1}{9}

Angenommen:

cos (x) = u

u^{2} = \frac{1}{9}

u^{2} = \frac{1}{9} : u = \frac{1}{3}, u = - \frac{1}{3}

u^{2} = \frac{1}{9}

Für

x^{2} = f (a)

sind die Lösungen

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

u = \frac{1}{9}, u = - \frac{1}{9}

\frac{1}{9} = \frac{1}{3}

\frac{1}{9}

Wende Radikal Regel an:

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

angenommen

a \geq 0, b \geq 0

= \frac{1}{9}

9 = 3

9

Faktorisiere die Zahl:

9 = 3^{2}

= 3^{2}

Wende Radikal Regel an:

n a^{n} = a

3^{2} = 3

= 3

= \frac{1}{3}

Wende Regel an

1 = 1

= \frac{1}{3}

- \frac{1}{9} = - \frac{1}{3}

- \frac{1}{9}

Vereinfache

\frac{1}{9} : \frac{1}{3}

\frac{1}{9}

Wende Radikal Regel an:

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

angenommen

a \geq 0, b \geq 0

= \frac{1}{9}

9 = 3

9

Faktorisiere die Zahl:

9 = 3^{2}

= 3^{2}

Wende Radikal Regel an:

n a^{n} = a

3^{2} = 3

= 3

= \frac{1}{3}

= - \frac{1}{3}

Wende Regel an

1 = 1

= - \frac{1}{3}

u = \frac{1}{3}, u = - \frac{1}{3}

Setze in

u = cos (x)

ein

cos (x) = \frac{1}{3}, cos (x) = - \frac{1}{3}

cos (x) = \frac{1}{3}, cos (x) = - \frac{1}{3}

cos (x) = \frac{1}{3} : x = arccos (\frac{1}{3}) + 2 πn, x = 2 π - arccos (\frac{1}{3}) + 2 πn

cos (x) = \frac{1}{3}

Wende die Eigenschaften der Trigonometrie an

cos (x) = \frac{1}{3}

Allgemeine Lösung für

cos (x) = \frac{1}{3}

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

x = arccos (\frac{1}{3}) + 2 πn, x = 2 π - arccos (\frac{1}{3}) + 2 πn

x = arccos (\frac{1}{3}) + 2 πn, x = 2 π - arccos (\frac{1}{3}) + 2 πn

cos (x) = - \frac{1}{3} : x = arccos (- \frac{1}{3}) + 2 πn, x = - arccos (- \frac{1}{3}) + 2 πn

cos (x) = - \frac{1}{3}

Wende die Eigenschaften der Trigonometrie an

cos (x) = - \frac{1}{3}

Allgemeine Lösung für

cos (x) = - \frac{1}{3}

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

x = arccos (- \frac{1}{3}) + 2 πn, x = - arccos (- \frac{1}{3}) + 2 πn

x = arccos (- \frac{1}{3}) + 2 πn, x = - arccos (- \frac{1}{3}) + 2 πn

Kombiniere alle Lösungen

x = arccos (\frac{1}{3}) + 2 πn, x = 2 π - arccos (\frac{1}{3}) + 2 πn, x = arccos (- \frac{1}{3}) + 2 πn, x = - arccos (- \frac{1}{3}) + 2 πn

Zeige Lösungen in Dezimalform

x = 1.23095 \dots + 2 πn, x = 2 π - 1.23095 \dots + 2 πn, x = 1.91063 \dots + 2 πn, x = - 1.91063 \dots + 2 πn

Graph

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