(sin(25)}{5.41}=\frac{sin(x))/9

Lösung

\frac{sin ( 2 5 ^{\circ} )}{5.41} = \frac{sin ( x )}{9}

x = 0.77969 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.77969 \dots + 36 0^{\circ} n

Radianten

x = 0.77969 \dots + 2 πn, x = π - 0.77969 \dots + 2 πn

Schritte zur Lösung

\frac{sin ( 2 5 ^{\circ} )}{5.41} = \frac{sin ( x )}{9}

Tausche die Seiten

\frac{sin ( x )}{9} = \frac{sin ( 2 5 ^{\circ} )}{5.41}

Multipliziere beide Seiten mit

9

\frac{sin ( x )}{9} = \frac{sin ( 2 5 ^{\circ} )}{5.41}

Multipliziere beide Seiten mit

9

\frac{9 sin ( x )}{9} = \frac{9 sin ( 2 5 ^{\circ} )}{5.41}

Vereinfache

sin (x) = \frac{9 sin ( 2 5 ^{\circ} )}{5.41}

sin (x) = \frac{9 sin ( 2 5 ^{\circ} )}{5.41}

Wende die Eigenschaften der Trigonometrie an

sin (x) = \frac{9 sin ( 2 5 ^{\circ} )}{5.41}

Allgemeine Lösung für

sin (x) = \frac{9 sin ( 2 5 ^{\circ} )}{5.41}

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

x = arcsin (\frac{9 sin ( 2 5 ^{\circ} )}{5.41}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{9 sin ( 2 5 ^{\circ} )}{5.41}) + 36 0^{\circ} n

x = arcsin (\frac{9 sin ( 2 5 ^{\circ} )}{5.41}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{9 sin ( 2 5 ^{\circ} )}{5.41}) + 36 0^{\circ} n

Zeige Lösungen in Dezimalform

x = 0.77969 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.77969 \dots + 36 0^{\circ} n

cos (θ) = \frac{4}{17}

- csc^{2} (x) + 2 csc (x) cot (x) = 0

6 sin (A) + 3 = 4 sin (A) + 4

so l v e f or a, - 10 = sin (a) + 15.2 cos (a)

0 = - 6 sin^{2} (θ) + 3 sin (θ) + 2