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sin(x)=(sin(45))/(1.3)

Lösung

sin (x) = \frac{sin ( 4 5 ^{\circ} )}{1.3}

x = 0.57511 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.57511 \dots + 36 0^{\circ} n

Radianten

x = 0.57511 \dots + 2 πn, x = π - 0.57511 \dots + 2 πn

Schritte zur Lösung

sin (x) = \frac{sin ( 4 5 ^{\circ} )}{1.3}

sin (4 5^{\circ}) = \frac{2}{2}

sin (4 5^{\circ})

Verwende die folgende triviale Identität:

sin (4 5^{\circ}) = \frac{2}{2}

sin (4 5^{\circ})

sin (x)

Periodizitätstabelle mit

36 0^{\circ} n

Zyklus:

= \frac{2}{2}

= \frac{2}{2}

sin (x) = \frac{\frac{2}{2}}{1.3}

Vereinfache

\frac{\frac{2}{2}}{1.3} : \frac{2}{2.6}

\frac{\frac{2}{2}}{1.3}

Wende Bruchregel an:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{2}{2 \cdot 1.3}

Multipliziere die Zahlen:

2 \cdot 1.3 = 2.6

= \frac{2}{2.6}

Wende die Eigenschaften der Trigonometrie an

sin (x) = \frac{2}{2.6}

Allgemeine Lösung für

sin (x) = \frac{2}{2.6}

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

x = arcsin (\frac{2}{2.6}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{2}{2.6}) + 36 0^{\circ} n

x = arcsin (\frac{2}{2.6}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{2}{2.6}) + 36 0^{\circ} n

Zeige Lösungen in Dezimalform

x = 0.57511 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.57511 \dots + 36 0^{\circ} n

arctan (x) + arctan (1 - x) = arctan (\frac{9}{7})

(2 cos (x) + 1) (sin (x) - 1) = 0

3 cos^{2} (θ) - sin^{2} (θ) = 0

sin (x) = (\frac{6}{4})

3 \cdot sin (x) + cos (x) = 3