sin(x)= 8/12

Lösung

sin (x) = \frac{8}{12}

x = 0.72972 \dots + 2 πn, x = π - 0.72972 \dots + 2 πn

Grad

x = 41.81031 \dots^{\circ} + 36 0^{\circ} n, x = 138.18968 \dots^{\circ} + 36 0^{\circ} n

Schritte zur Lösung

sin (x) = \frac{8}{12}

Streiche die gemeinsamen Faktoren:

4

sin (x) = \frac{2}{3}

Wende die Eigenschaften der Trigonometrie an

sin (x) = \frac{2}{3}

Allgemeine Lösung für

sin (x) = \frac{2}{3}

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

x = arcsin (\frac{2}{3}) + 2 πn, x = π - arcsin (\frac{2}{3}) + 2 πn

x = arcsin (\frac{2}{3}) + 2 πn, x = π - arcsin (\frac{2}{3}) + 2 πn

Zeige Lösungen in Dezimalform

x = 0.72972 \dots + 2 πn, x = π - 0.72972 \dots + 2 πn

2 - 2 sin (θ) = 4

tan^{2} (x) sin (x) - \frac{sin ( x )}{3} = 0

1 + cot^{2} (x) = 8 sin (x)

4 sin^{2} (x) = 8 sin^{2} (\frac{x}{2})

cos (\frac{π}{2} - x) = 0