cos(θ)=(-1)/2 ,0<= θ<= 4pi

Lösung

cos (θ) = \frac{- 1}{2}, 0 \leq θ \leq 4 π

θ = \frac{2 π}{3}, θ = \frac{4 π}{3}, θ = \frac{8 π}{3}, θ = \frac{10 π}{3}

Grad

θ = 12 0^{\circ}, θ = 24 0^{\circ}, θ = 48 0^{\circ}, θ = 60 0^{\circ}

Schritte zur Lösung

cos (θ) = \frac{- 1}{2}, 0 \leq θ \leq 4 π

Wende Bruchregel an:

\frac{- a}{b} = - \frac{a}{b}

cos (θ) = - \frac{1}{2}

Allgemeine Lösung für

cos (θ) = - \frac{1}{2}

cos (x)

Periodizitätstabelle mit

2 πn

Zyklus:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

θ = \frac{2 π}{3} + 2 πn, θ = \frac{4 π}{3} + 2 πn

θ = \frac{2 π}{3} + 2 πn, θ = \frac{4 π}{3} + 2 πn

Lösungen für den Bereich

0 \leq θ \leq 4 π

θ = \frac{2 π}{3}, θ = \frac{4 π}{3}, θ = \frac{8 π}{3}, θ = \frac{10 π}{3}

20 sin^{2} (x) + 27 cos (x) = 6

- 8 csc^{2} (x) - 4 cot (x) = - 12

sin (2 x) + 2 cos^{2} (x) = 0

sin (θ) = \frac{5}{3}

14 sin^{2} (x) + 5 sin (x) - 1 = 0