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sin(2x)=0.8,-180<= x<= 180

Lösung

sin (2 x) = 0.8, - 18 0^{\circ} \leq x \leq 18 0^{\circ}

x = 0.46364 \dots, x = \frac{18 0 ^{\circ} - 0.92729 \dots}{2}, x = - 2.67794 \dots, x = \frac{- 18 0 ^{\circ} - 0.92729 \dots}{2}

Radianten

x = 0.46364 \dots, x = \frac{π - 0.92729 \dots}{2}, x = - 2.67794 \dots, x = \frac{- π - 0.92729 \dots}{2}

Schritte zur Lösung

sin (2 x) = 0.8, - 18 0^{\circ} \leq x \leq 18 0^{\circ}

Wende die Eigenschaften der Trigonometrie an

sin (2 x) = 0.8

Allgemeine Lösung für

sin (2 x) = 0.8

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

2 x = arcsin (0.8) + 36 0^{\circ} n, 2 x = 18 0^{\circ} - arcsin (0.8) + 36 0^{\circ} n

2 x = arcsin (0.8) + 36 0^{\circ} n, 2 x = 18 0^{\circ} - arcsin (0.8) + 36 0^{\circ} n

Löse

2 x = arcsin (0.8) + 36 0^{\circ} n : x = \frac{arcsin ( 0.8 )}{2} + 18 0^{\circ} n

2 x = arcsin (0.8) + 36 0^{\circ} n

Teile beide Seiten durch

2

2 x = arcsin (0.8) + 36 0^{\circ} n

Teile beide Seiten durch

2

\frac{2 x}{2} = \frac{arcsin ( 0.8 )}{2} + \frac{36 0 ^{\circ} n}{2}

Vereinfache

x = \frac{arcsin ( 0.8 )}{2} + 18 0^{\circ} n

x = \frac{arcsin ( 0.8 )}{2} + 18 0^{\circ} n

Löse

2 x = 18 0^{\circ} - arcsin (0.8) + 36 0^{\circ} n : x = 9 0^{\circ} - \frac{arcsin ( 0.8 )}{2} + 18 0^{\circ} n

2 x = 18 0^{\circ} - arcsin (0.8) + 36 0^{\circ} n

Teile beide Seiten durch

2

2 x = 18 0^{\circ} - arcsin (0.8) + 36 0^{\circ} n

Teile beide Seiten durch

2

\frac{2 x}{2} = 9 0^{\circ} - \frac{arcsin ( 0.8 )}{2} + \frac{36 0 ^{\circ} n}{2}

Vereinfache

x = 9 0^{\circ} - \frac{arcsin ( 0.8 )}{2} + 18 0^{\circ} n

x = 9 0^{\circ} - \frac{arcsin ( 0.8 )}{2} + 18 0^{\circ} n

x = \frac{arcsin ( 0.8 )}{2} + 18 0^{\circ} n, x = 9 0^{\circ} - \frac{arcsin ( 0.8 )}{2} + 18 0^{\circ} n

Lösungen für den Bereich

- 18 0^{\circ} \leq x \leq 18 0^{\circ}

x = 0.46364 \dots, x = \frac{18 0 ^{\circ} - 0.92729 \dots}{2}, x = - 2.67794 \dots, x = \frac{- 18 0 ^{\circ} - 0.92729 \dots}{2}

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

cos^{2} (t) - 3 sin (t) = 3

4 sin^{4} (x) - 4 sin^{2} (x) + 1 = 0

(1.33) sin (2 5^{\circ}) = (1.5) sin (θ)

so l v e f or t, y = cos (2 t)