(sin(x))/(25)=(sin(125))/(165.6)

Lösung

\frac{sin ( x )}{25} = \frac{sin ( 12 5 ^{\circ} )}{165.6}

x = 0.12398 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.12398 \dots + 36 0^{\circ} n

Radianten

x = 0.12398 \dots + 2 πn, x = π - 0.12398 \dots + 2 πn

Schritte zur Lösung

\frac{sin ( x )}{25} = \frac{sin ( 12 5 ^{\circ} )}{165.6}

Multipliziere beide Seiten mit

25

\frac{sin ( x )}{25} = \frac{sin ( 12 5 ^{\circ} )}{165.6}

Multipliziere beide Seiten mit

25

\frac{25 sin ( x )}{25} = \frac{25 sin ( 12 5 ^{\circ} )}{165.6}

Vereinfache

sin (x) = \frac{25 sin ( 12 5 ^{\circ} )}{165.6}

sin (x) = \frac{25 sin ( 12 5 ^{\circ} )}{165.6}

Wende die Eigenschaften der Trigonometrie an

sin (x) = \frac{25 sin ( 12 5 ^{\circ} )}{165.6}

Allgemeine Lösung für

sin (x) = \frac{25 sin ( 12 5 ^{\circ} )}{165.6}

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

x = arcsin (\frac{25 sin ( 12 5 ^{\circ} )}{165.6}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{25 sin ( 12 5 ^{\circ} )}{165.6}) + 36 0^{\circ} n

x = arcsin (\frac{25 sin ( 12 5 ^{\circ} )}{165.6}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{25 sin ( 12 5 ^{\circ} )}{165.6}) + 36 0^{\circ} n

Zeige Lösungen in Dezimalform

x = 0.12398 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.12398 \dots + 36 0^{\circ} n

2 cos (3 θ) - 1 = 0

cos (4 x) = cos (8 x)

cos (2 x) - cos (x) = 2

4 sin (2 x) + 23 = 0

so l v e f or x, 3 = 18 cos (x)