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Beliebt Trigonometrie >

2cos^4(x)cos(x)-cos^5(x)=1

Lösung

2 cos^{4} (x) cos (x) - cos^{5} (x) = 1

Lösung

x = 2 πn

+1

Grad

x = 0^{\circ} + 36 0^{\circ} n

Schritte zur Lösung

2 cos^{4} (x) cos (x) - cos^{5} (x) = 1

Vereinfache

2 cos^{4} (x) cos (x) - cos^{5} (x) : cos^{5} (x)

2 cos^{4} (x) cos (x) - cos^{5} (x)

2 cos^{4} (x) cos (x) = 2 cos^{5} (x)

2 cos^{4} (x) cos (x)

Wende Exponentenregel an:

a^{b} \cdot a^{c} = a^{b + c}

cos^{4} (x) cos (x) = cos^{4 + 1} (x)

= 2 cos^{4 + 1} (x)

Addiere die Zahlen:

4 + 1 = 5

= 2 cos^{5} (x)

= 2 cos^{5} (x) - cos^{5} (x)

Addiere gleiche Elemente:

2 cos^{5} (x) - cos^{5} (x) = cos^{5} (x)

= cos^{5} (x)

cos^{5} (x) = 1

Für

x^{n} = f (a)

, n ist ungerade, die Lösung ist

x = n f (a)

cos (x) = 51

51 = 1

51

Wende Regel an

n 1 = 1

= 1

cos (x) = 1

Allgemeine Lösung für

cos (x) = 1

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 = 0 + 2 πn

x = 0 + 2 πn

Löse

x = 0 + 2 πn : x = 2 πn

x = 0 + 2 πn

0 + 2 πn = 2 πn

x = 2 πn

x = 2 πn

Graph

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