cos(t)= 1/2

Lösung

cos (t) = \frac{1}{2}

t = \frac{π}{3} + 2 πn, t = \frac{5 π}{3} + 2 πn

Grad

t = 6 0^{\circ} + 36 0^{\circ} n, t = 30 0^{\circ} + 36 0^{\circ} n

Schritte zur Lösung

cos (t) = \frac{1}{2}

Allgemeine Lösung für

cos (t) = \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}

t = \frac{π}{3} + 2 πn, t = \frac{5 π}{3} + 2 πn

t = \frac{π}{3} + 2 πn, t = \frac{5 π}{3} + 2 πn

cos (x) = 2

6 cos^{2} (x) - 7 sin (x) - 1 = 0

2 sin^{2} (θ) + 3 sin (θ) + 1 = 0

1 = sin (x)

sin (2 x) = - cos (x)