cos(x)= 1/2 sqrt(3)

Lösung

cos (x) = \frac{1}{2} 3

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

Schritte zur Lösung

cos (x) = \frac{1}{2} 3

Vereinfache

\frac{1}{2} 3 : \frac{3}{2}

\frac{1}{2} 3

Multipliziere Brüche:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot 3}{2}

Multipliziere:

1 \cdot 3 = 3

= \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

sin (2 x - 1 0^{\circ}) = cos (x + 4 0^{\circ})

2 sec^{2} (x) - 8 = 0

sin (x) - 2 cos (2 x) = - \frac{1}{2}

4 cos^{4} (x) - 1 = 0

arccos (2 x) - arccos (x) = \frac{π}{3}