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Beliebt Trigonometrie >

2sin^2(t)cos(t)=0

Lösung

2 sin^{2} (t) cos (t) = 0

Lösung

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

+1

Grad

t = 0^{\circ} + 36 0^{\circ} n, t = 18 0^{\circ} + 36 0^{\circ} n, t = 9 0^{\circ} + 36 0^{\circ} n, t = 27 0^{\circ} + 36 0^{\circ} n

Schritte zur Lösung

2 sin^{2} (t) cos (t) = 0

Löse jeden Teil einzeln

sin^{2} (t) = 0 or cos (t) = 0

sin^{2} (t) = 0 : t = 2 πn, t = π + 2 πn

sin^{2} (t) = 0

Wende Regel an

x^{n} = 0 \Rightarrow x = 0

sin (t) = 0

Allgemeine Lösung für

sin (t) = 0

sin (x)

Periodizitätstabelle mit

2 πn

Zyklus:

t = 0 + 2 πn, t = π + 2 πn

t = 0 + 2 πn, t = π + 2 πn

Löse

t = 0 + 2 πn : t = 2 πn

t = 0 + 2 πn

0 + 2 πn = 2 πn

t = 2 πn

t = 2 πn, t = π + 2 πn

cos (t) = 0 : t = \frac{π}{2} + 2 πn, t = \frac{3 π}{2} + 2 πn

cos (t) = 0

Allgemeine Lösung für

cos (t) = 0

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}{2} + 2 πn, t = \frac{3 π}{2} + 2 πn

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

Kombiniere alle Lösungen

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

Graph

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arctan(e^x)= pi/4

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