solvefor θ,cos(θ)= 6/(sqrt(85))

Lösung

löse nach

θ, cos (θ) = \frac{6}{85}

θ = 0.86217 \dots + 2 πn, θ = 2 π - 0.86217 \dots + 2 πn

Radianten

θ = 0.86217 \dots + 6.28318 \dots n, θ = 5.42101 \dots + 6.28318 \dots n

Schritte zur Lösung

cos (θ) = \frac{6}{85}

Vereinfache

\frac{6}{85} : \frac{6 85}{85}

\frac{6}{85}

Multipliziere mit dem Konjugat

\frac{85}{85}

= \frac{6 85}{85 85}

8585 = 85

8585

Wende Radikal Regel an:

a a = a

8585 = 85

= 85

= \frac{6 85}{85}

cos (θ) = \frac{6 85}{85}

Wende die Eigenschaften der Trigonometrie an

cos (θ) = \frac{6 85}{85}

Allgemeine Lösung für

cos (θ) = \frac{6 85}{85}

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

θ = arccos (\frac{6 85}{85}) + 2 πn, θ = 2 π - arccos (\frac{6 85}{85}) + 2 πn

θ = arccos (\frac{6 85}{85}) + 2 πn, θ = 2 π - arccos (\frac{6 85}{85}) + 2 πn

Zeige Lösungen in Dezimalform

θ = 0.86217 \dots + 2 πn, θ = 2 π - 0.86217 \dots + 2 πn

6 sin^{2} (x) - 3 = 0

2 cos^{2} (θ) = sin (θ) + 1

tan^{2} (2 x) = \frac{1}{3}

- 8 cos (x) - 7 = 0

3 sin (2 x) - 3 cos (x) = 0