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

Lösung

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

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

Radianten

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

Schritte zur Lösung

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

Tausche die Seiten

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

Multipliziere beide Seiten mit

4

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

Multipliziere beide Seiten mit

4

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

Vereinfache

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

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

Wende die Eigenschaften der Trigonometrie an

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

Allgemeine Lösung für

sin (x) = \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

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

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

Zeige Lösungen in Dezimalform

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

\frac{cos ( x )}{cot ( x )} = sec (x)

sin (x) = - 0.61

cos (2 x) - sin (- x) = 0

6 cos^{2} (x) + cos (2 x) = 1

sin (2 π t) = 1