sin(x)= 10/12

Lösung

sin (x) = \frac{10}{12}

x = 0.98511 \dots + 2 πn, x = π - 0.98511 \dots + 2 πn

Grad

x = 56.44269 \dots^{\circ} + 36 0^{\circ} n, x = 123.55730 \dots^{\circ} + 36 0^{\circ} n

Schritte zur Lösung

sin (x) = \frac{10}{12}

Streiche die gemeinsamen Faktoren:

2

sin (x) = \frac{5}{6}

Wende die Eigenschaften der Trigonometrie an

sin (x) = \frac{5}{6}

Allgemeine Lösung für

sin (x) = \frac{5}{6}

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

x = arcsin (\frac{5}{6}) + 2 πn, x = π - arcsin (\frac{5}{6}) + 2 πn

x = arcsin (\frac{5}{6}) + 2 πn, x = π - arcsin (\frac{5}{6}) + 2 πn

Zeige Lösungen in Dezimalform

x = 0.98511 \dots + 2 πn, x = π - 0.98511 \dots + 2 πn

3 cot (x) = - 1, 0 \leq x \leq 2 π

sin (x) = \frac{10}{14}

cos (x) = \frac{9}{15}

8 sin^{2} (x) + 12 sin (x) + 4 = 0

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