(sin(65))/5 =(sin(x))/4

Lösung

\frac{sin ( 6 5 ^{\circ} )}{5} = \frac{sin ( x )}{4}

x = 0.81110 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.81110 \dots + 36 0^{\circ} n

Radianten

x = 0.81110 \dots + 2 πn, x = π - 0.81110 \dots + 2 πn

Schritte zur Lösung

\frac{sin ( 6 5 ^{\circ} )}{5} = \frac{sin ( x )}{4}

Tausche die Seiten

\frac{sin ( x )}{4} = \frac{sin ( 6 5 ^{\circ} )}{5}

Multipliziere beide Seiten mit

4

\frac{sin ( x )}{4} = \frac{sin ( 6 5 ^{\circ} )}{5}

Multipliziere beide Seiten mit

4

\frac{4 sin ( x )}{4} = \frac{4 sin ( 6 5 ^{\circ} )}{5}

Vereinfache

sin (x) = \frac{4 sin ( 6 5 ^{\circ} )}{5}

sin (x) = \frac{4 sin ( 6 5 ^{\circ} )}{5}

Wende die Eigenschaften der Trigonometrie an

sin (x) = \frac{4 sin ( 6 5 ^{\circ} )}{5}

Allgemeine Lösung für

sin (x) = \frac{4 sin ( 6 5 ^{\circ} )}{5}

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

x = arcsin (\frac{4 sin ( 6 5 ^{\circ} )}{5}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{4 sin ( 6 5 ^{\circ} )}{5}) + 36 0^{\circ} n

x = arcsin (\frac{4 sin ( 6 5 ^{\circ} )}{5}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{4 sin ( 6 5 ^{\circ} )}{5}) + 36 0^{\circ} n

Zeige Lösungen in Dezimalform

x = 0.81110 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.81110 \dots + 36 0^{\circ} n

1.33 \cdot sin (6 0^{\circ}) = 1.52 \cdot sin (x)

tan (x) = - 3 cos (x) tan (x)

tan (x - \frac{π}{4}) = \frac{1}{6}

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

arccos (\frac{3}{2}) + arcsin (3 x) = \frac{π}{2}