cos^5(x)= 1/2

Lösung

cos^{5} (x) = \frac{1}{2}

x = 0.51447 \dots + 2 πn, x = 2 π - 0.51447 \dots + 2 πn

Grad

x = 29.47731 \dots^{\circ} + 36 0^{\circ} n, x = 330.52268 \dots^{\circ} + 36 0^{\circ} n

Schritte zur Lösung

cos^{5} (x) = \frac{1}{2}

Für

x^{n} = f (a)

, n ist ungerade, die Lösung ist

x = n f (a)

cos (x) = 5 \frac{1}{2}

Wende die Eigenschaften der Trigonometrie an

cos (x) = 5 \frac{1}{2}

Allgemeine Lösung für

cos (x) = 5 \frac{1}{2}

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = 2 π - arccos (a) + 2 πn

x = arccos (5 \frac{1}{2}) + 2 πn, x = 2 π - arccos (5 \frac{1}{2}) + 2 πn

x = arccos (5 \frac{1}{2}) + 2 πn, x = 2 π - arccos (5 \frac{1}{2}) + 2 πn

Zeige Lösungen in Dezimalform

x = 0.51447 \dots + 2 πn, x = 2 π - 0.51447 \dots + 2 πn

\frac{cos ^{2022} ( x )}{( sin ^{2022} ( x ) + cos ^{2022} ( x ) )} = 1

5 sec (x) - 4 cos (x) = 8

sin^{3} (x) = - 1

so l v e f or x, sin^{2} (x) = \frac{( 1 - cos ( y ) )}{2}

sin (x) + sin^{2} (x) + cos (x) + cos^{2} (x) = 0