cos(θ)= 1/(sqrt(6))

Lösung

cos (θ) = \frac{1}{6}

θ = 1.15026 \dots + 2 πn, θ = 2 π - 1.15026 \dots + 2 πn

Radianten

θ = 1.15026 \dots + 6.28318 \dots n, θ = 5.13292 \dots + 6.28318 \dots n

Schritte zur Lösung

cos (θ) = \frac{1}{6}

Vereinfache

\frac{1}{6} : \frac{6}{6}

\frac{1}{6}

Multipliziere mit dem Konjugat

\frac{6}{6}

= \frac{1 \cdot 6}{6 6}

1 \cdot 6 = 6

66 = 6

66

Wende Radikal Regel an:

a a = a

66 = 6

= 6

= \frac{6}{6}

cos (θ) = \frac{6}{6}

Wende die Eigenschaften der Trigonometrie an

cos (θ) = \frac{6}{6}

Allgemeine Lösung für

cos (θ) = \frac{6}{6}

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

θ = arccos (\frac{6}{6}) + 2 πn, θ = 2 π - arccos (\frac{6}{6}) + 2 πn

θ = arccos (\frac{6}{6}) + 2 πn, θ = 2 π - arccos (\frac{6}{6}) + 2 πn

Zeige Lösungen in Dezimalform

θ = 1.15026 \dots + 2 πn, θ = 2 π - 1.15026 \dots + 2 πn

4 tan^{2} (θ) = - 3 tan (θ) + tan^{2} (θ)

2 sec^{2} (x) - 3 tan (x) = 11

3 cos (2 x) = - 3

4 cos^{2} (θ) + cos (2 θ) - 7 cos (θ) = - 2

sec^{2} (θ) + 2 sec (θ) = 8