cos(θ)= 1/(sqrt(5))

Lösung

cos (θ) = \frac{1}{5}

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

Radianten

θ = 1.10714 \dots + 6.28318 \dots n, θ = 5.17603 \dots + 6.28318 \dots n

Schritte zur Lösung

cos (θ) = \frac{1}{5}

Vereinfache

\frac{1}{5} : \frac{5}{5}

\frac{1}{5}

Multipliziere mit dem Konjugat

\frac{5}{5}

= \frac{1 \cdot 5}{5 5}

1 \cdot 5 = 5

55 = 5

55

Wende Radikal Regel an:

a a = a

55 = 5

= 5

= \frac{5}{5}

cos (θ) = \frac{5}{5}

Wende die Eigenschaften der Trigonometrie an

cos (θ) = \frac{5}{5}

Allgemeine Lösung für

cos (θ) = \frac{5}{5}

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

θ = arccos (\frac{5}{5}) + 2 πn, θ = 2 π - arccos (\frac{5}{5}) + 2 πn

θ = arccos (\frac{5}{5}) + 2 πn, θ = 2 π - arccos (\frac{5}{5}) + 2 πn

Zeige Lösungen in Dezimalform

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

cos (x) = \frac{4}{10}

16 cos (2 x) - 4 = 0

- csc (x) cot (x) = 0

4 sin (θ) = \frac{1}{cos ( θ )}

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