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Beliebt Trigonometrie >

|cos(x)|=(sqrt(3))/2

Lösung

∣ cos (x) ∣ = \frac{3}{2}

Lösung

x = \frac{5 π}{6} + 2 πn, x = \frac{7 π}{6} + 2 πn, x = \frac{π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

+1

Grad

x = 15 0^{\circ} + 36 0^{\circ} n, x = 21 0^{\circ} + 36 0^{\circ} n, x = 3 0^{\circ} + 36 0^{\circ} n, x = 33 0^{\circ} + 36 0^{\circ} n

Schritte zur Lösung

∣ cos (x) ∣ = \frac{3}{2}

Löse mit Substitution

∣ cos (x) ∣ = \frac{3}{2}

Angenommen:

cos (x) = u

∣ u ∣ = \frac{3}{2}

∣ u ∣ = \frac{3}{2} : u = - \frac{3}{2} or u = \frac{3}{2}

∣ u ∣ = \frac{3}{2}

Wende Absoluteregel an: Wenn

∣ u ∣ = a, a > 0

dann

u = a

or

u = - a

u = - \frac{3}{2} or u = \frac{3}{2}

Setze in

u = cos (x)

ein

cos (x) = - \frac{3}{2} or cos (x) = \frac{3}{2}

cos (x) = - \frac{3}{2} or cos (x) = \frac{3}{2}

cos (x) = - \frac{3}{2} : x = \frac{5 π}{6} + 2 πn, x = \frac{7 π}{6} + 2 πn

cos (x) = - \frac{3}{2}

Allgemeine Lösung für

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

x = \frac{5 π}{6} + 2 πn, x = \frac{7 π}{6} + 2 πn

x = \frac{5 π}{6} + 2 πn, x = \frac{7 π}{6} + 2 πn

cos (x) = \frac{3}{2} : x = \frac{π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

cos (x) = \frac{3}{2}

Allgemeine Lösung für

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

x = \frac{π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

x = \frac{π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

Kombiniere alle Lösungen

x = \frac{5 π}{6} + 2 πn, x = \frac{7 π}{6} + 2 πn, x = \frac{π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

Graph

Beliebte Beispiele

tan(θ)=(-1)/(sqrt(3)),0<= θ<= 360

tan (θ) = \frac{- 1}{3}, 0^{\circ} \leq θ \leq 36 0^{\circ}

tan((91pi)/(36))=cos(360-x)

tan (\frac{91 π}{36}) = cos (36 0^{\circ} - x)

2sin(3x-pi/6)+sqrt(3)=0

2 sin (3 x - \frac{π}{6}) + 3 = 0

12=3sec(θ)+5csc(θ)

12 = 3 sec (θ) + 5 csc (θ)

sin(9x+2)=cos(6x-7)

sin (9 x + 2) = cos (6 x - 7)