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sec^2(x)=(3sqrt(3))/pi

Lösung

sec^{2} (x) = \frac{3 3}{π}

x = 0.68001 \dots + 2 πn, x = 2 π - 0.68001 \dots + 2 πn, x = 2.46157 \dots + 2 πn, x = - 2.46157 \dots + 2 πn

Grad

x = 38.96227 \dots^{\circ} + 36 0^{\circ} n, x = 321.03772 \dots^{\circ} + 36 0^{\circ} n, x = 141.03772 \dots^{\circ} + 36 0^{\circ} n, x = - 141.03772 \dots^{\circ} + 36 0^{\circ} n

Schritte zur Lösung

sec^{2} (x) = \frac{3 3}{π}

Löse mit Substitution

sec^{2} (x) = \frac{3 3}{π}

Angenommen:

sec (x) = u

u^{2} = \frac{3 3}{π}

u^{2} = \frac{3 3}{π} : u = \frac{3 3}{π}, u = - \frac{3 3}{π}

u^{2} = \frac{3 3}{π}

Für

x^{2} = f (a)

sind die Lösungen

x = f (a), - f (a)

u = \frac{3 3}{π}, u = - \frac{3 3}{π}

Setze in

u = sec (x)

ein

sec (x) = \frac{3 3}{π}, sec (x) = - \frac{3 3}{π}

sec (x) = \frac{3 3}{π}, sec (x) = - \frac{3 3}{π}

sec (x) = \frac{3 3}{π} : x = arcsec \frac{3 3}{π} + 2 πn, x = 2 π - arcsec \frac{3 3}{π} + 2 πn

sec (x) = \frac{3 3}{π}

Wende die Eigenschaften der Trigonometrie an

sec (x) = \frac{3 3}{π}

Allgemeine Lösung für

sec (x) = \frac{3 3}{π}

sec (x) = a \Rightarrow x = arcsec (a) + 2 πn, x = 2 π - arcsec (a) + 2 πn

x = arcsec \frac{3 3}{π} + 2 πn, x = 2 π - arcsec \frac{3 3}{π} + 2 πn

x = arcsec \frac{3 3}{π} + 2 πn, x = 2 π - arcsec \frac{3 3}{π} + 2 πn

sec (x) = - \frac{3 3}{π} : x = arcsec - \frac{3 3}{π} + 2 πn, x = - arcsec - \frac{3 3}{π} + 2 πn

sec (x) = - \frac{3 3}{π}

Wende die Eigenschaften der Trigonometrie an

sec (x) = - \frac{3 3}{π}

Allgemeine Lösung für

sec (x) = - \frac{3 3}{π}

sec (x) = - a \Rightarrow x = arcsec (- a) + 2 πn, x = - arcsec (- a) + 2 πn

x = arcsec - \frac{3 3}{π} + 2 πn, x = - arcsec - \frac{3 3}{π} + 2 πn

x = arcsec - \frac{3 3}{π} + 2 πn, x = - arcsec - \frac{3 3}{π} + 2 πn

Kombiniere alle Lösungen

x = arcsec \frac{3 3}{π} + 2 πn, x = 2 π - arcsec \frac{3 3}{π} + 2 πn, x = arcsec - \frac{3 3}{π} + 2 πn, x = - arcsec - \frac{3 3}{π} + 2 πn

Zeige Lösungen in Dezimalform

x = 0.68001 \dots + 2 πn, x = 2 π - 0.68001 \dots + 2 πn, x = 2.46157 \dots + 2 πn, x = - 2.46157 \dots + 2 πn

sin (θ) (sin (θ) + 1) = 0

6 tan^{2} (x) + 13 tan (x) + 6 = 0

0 = arctan (x) + \frac{π}{2}

2 tan^{2} (θ) = sec^{2} (θ) + 2

5^{s i n (2 x - \frac{x}{4})} = 1