sin(x)=(6sin(20))/4

Lösung

sin (x) = \frac{6 sin ( 2 0 ^{\circ} )}{4}

x = 0.53871 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.53871 \dots + 36 0^{\circ} n

Radianten

x = 0.53871 \dots + 2 πn, x = π - 0.53871 \dots + 2 πn

Schritte zur Lösung

sin (x) = \frac{6 sin ( 2 0 ^{\circ} )}{4}

Streiche die gemeinsamen Faktoren:

2

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

Wende die Eigenschaften der Trigonometrie an

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

Allgemeine Lösung für

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

sin (x) = a \Rightarrow x = arcsin (a) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (a) + 36 0^{\circ} n

x = arcsin (\frac{3 sin ( 2 0 ^{\circ} )}{2}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{3 sin ( 2 0 ^{\circ} )}{2}) + 36 0^{\circ} n

x = arcsin (\frac{3 sin ( 2 0 ^{\circ} )}{2}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{3 sin ( 2 0 ^{\circ} )}{2}) + 36 0^{\circ} n

Zeige Lösungen in Dezimalform

x = 0.53871 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.53871 \dots + 36 0^{\circ} n

0 = 1.2209 \cdot cos (x) + 0.0422 \cdot cos (2 \cdot x)

5 sin (θ) + 3 = 0

cos^{2} (x) - sin^{2} (x) = 2 cos (x) - 1

cos (x) + cos (2 x) = - 1

cos (θ) = \frac{6}{3 5}