(sin(74))/8 =(sin(a))/4

Lösung

\frac{sin ( 7 4 ^{\circ} )}{8} = \frac{sin ( a )}{4}

a = 0.50137 \dots + 36 0^{\circ} n, a = 18 0^{\circ} - 0.50137 \dots + 36 0^{\circ} n

Radianten

a = 0.50137 \dots + 2 πn, a = π - 0.50137 \dots + 2 πn

Schritte zur Lösung

\frac{sin ( 7 4 ^{\circ} )}{8} = \frac{sin ( a )}{4}

Tausche die Seiten

\frac{sin ( a )}{4} = \frac{sin ( 7 4 ^{\circ} )}{8}

Multipliziere beide Seiten mit

4

\frac{sin ( a )}{4} = \frac{sin ( 7 4 ^{\circ} )}{8}

Multipliziere beide Seiten mit

4

\frac{4 sin ( a )}{4} = \frac{4 sin ( 7 4 ^{\circ} )}{8}

Vereinfache

sin (a) = \frac{sin ( 7 4 ^{\circ} )}{2}

sin (a) = \frac{sin ( 7 4 ^{\circ} )}{2}

Wende die Eigenschaften der Trigonometrie an

sin (a) = \frac{sin ( 7 4 ^{\circ} )}{2}

Allgemeine Lösung für

sin (a) = \frac{sin ( 7 4 ^{\circ} )}{2}

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

a = arcsin (\frac{sin ( 7 4 ^{\circ} )}{2}) + 36 0^{\circ} n, a = 18 0^{\circ} - arcsin (\frac{sin ( 7 4 ^{\circ} )}{2}) + 36 0^{\circ} n

a = arcsin (\frac{sin ( 7 4 ^{\circ} )}{2}) + 36 0^{\circ} n, a = 18 0^{\circ} - arcsin (\frac{sin ( 7 4 ^{\circ} )}{2}) + 36 0^{\circ} n

Zeige Lösungen in Dezimalform

a = 0.50137 \dots + 36 0^{\circ} n, a = 18 0^{\circ} - 0.50137 \dots + 36 0^{\circ} n

sin (x) = sin (x - \frac{π}{2})

tan (x) = \frac{π}{3}

cos (x) = - 0.58

tan^{4} (x) - 4 tan^{2} (x) + 3 = 0

sin (2 x) = \frac{21}{25}