sin(x)= 10/14

Lösung

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

x = 0.79560 \dots + 2 πn, x = π - 0.79560 \dots + 2 πn

Grad

x = 45.58469 \dots^{\circ} + 36 0^{\circ} n, x = 134.41530 \dots^{\circ} + 36 0^{\circ} n

Schritte zur Lösung

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

Streiche die gemeinsamen Faktoren:

2

sin (x) = \frac{5}{7}

Wende die Eigenschaften der Trigonometrie an

sin (x) = \frac{5}{7}

Allgemeine Lösung für

sin (x) = \frac{5}{7}

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

x = arcsin (\frac{5}{7}) + 2 πn, x = π - arcsin (\frac{5}{7}) + 2 πn

x = arcsin (\frac{5}{7}) + 2 πn, x = π - arcsin (\frac{5}{7}) + 2 πn

Zeige Lösungen in Dezimalform

x = 0.79560 \dots + 2 πn, x = π - 0.79560 \dots + 2 πn

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

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

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

0 = 4 sin (x)

sec^{2} (θ) (1 + cos^{2} (θ)) = 2 - tan^{2} (θ)