(sin(47))/(12)=(sin(x))/(11)

Lösung

\frac{sin ( 4 7 ^{\circ} )}{12} = \frac{sin ( x )}{11}

x = 0.73475 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.73475 \dots + 36 0^{\circ} n

Radianten

x = 0.73475 \dots + 2 πn, x = π - 0.73475 \dots + 2 πn

Schritte zur Lösung

\frac{sin ( 4 7 ^{\circ} )}{12} = \frac{sin ( x )}{11}

Tausche die Seiten

\frac{sin ( x )}{11} = \frac{sin ( 4 7 ^{\circ} )}{12}

Multipliziere beide Seiten mit

11

\frac{sin ( x )}{11} = \frac{sin ( 4 7 ^{\circ} )}{12}

Multipliziere beide Seiten mit

11

\frac{11 sin ( x )}{11} = \frac{11 sin ( 4 7 ^{\circ} )}{12}

Vereinfache

sin (x) = \frac{11 sin ( 4 7 ^{\circ} )}{12}

sin (x) = \frac{11 sin ( 4 7 ^{\circ} )}{12}

Wende die Eigenschaften der Trigonometrie an

sin (x) = \frac{11 sin ( 4 7 ^{\circ} )}{12}

Allgemeine Lösung für

sin (x) = \frac{11 sin ( 4 7 ^{\circ} )}{12}

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

x = arcsin (\frac{11 sin ( 4 7 ^{\circ} )}{12}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{11 sin ( 4 7 ^{\circ} )}{12}) + 36 0^{\circ} n

x = arcsin (\frac{11 sin ( 4 7 ^{\circ} )}{12}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{11 sin ( 4 7 ^{\circ} )}{12}) + 36 0^{\circ} n

Zeige Lösungen in Dezimalform

x = 0.73475 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.73475 \dots + 36 0^{\circ} n

cos (2 x) + 3 cos (x) = - 1

2 cos (α) = 3

3 tan (x) - 2 sin (x) = 0

2 sin^{2} (2 x) - cos (2 x) - 1 = 0

cos (x) + 3 sin (x) = 2