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sec(x)sin(x)-3sin(x)=0,0<= x<= 360

Lösung

sec (x) sin (x) - 3 sin (x) = 0, 0 \leq x \leq 36 0^{\circ}

x = 0, x = 18 0^{\circ}, x = 36 0^{\circ}, x = 1.23095 \dots, x = 36 0^{\circ} - 1.23095 \dots

Radianten

x = 0, x = π, x = 2 π, x = 1.23095 \dots, x = 2 π - 1.23095 \dots

Schritte zur Lösung

sec (x) sin (x) - 3 sin (x) = 0, 0 \leq x \leq 36 0^{\circ}

Faktorisiere

sec (x) sin (x) - 3 sin (x) : sin (x) (sec (x) - 3)

sec (x) sin (x) - 3 sin (x)

Klammere gleiche Terme aus

sin (x)

= sin (x) (sec (x) - 3)

sin (x) (sec (x) - 3) = 0

Löse jeden Teil einzeln

sin (x) = 0 or sec (x) - 3 = 0

sin (x) = 0, 0 \leq x \leq 36 0^{\circ} : x = 0, x = 18 0^{\circ}, x = 36 0^{\circ}

sin (x) = 0, 0 \leq x \leq 36 0^{\circ}

Allgemeine Lösung für

sin (x) = 0

sin (x)

Periodizitätstabelle mit

36 0^{\circ} n

Zyklus:

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

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

Löse

x = 0 + 36 0^{\circ} n : x = 36 0^{\circ} n

x = 0 + 36 0^{\circ} n

0 + 36 0^{\circ} n = 36 0^{\circ} n

x = 36 0^{\circ} n

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

Lösungen für den Bereich

0 \leq x \leq 36 0^{\circ}

x = 0, x = 18 0^{\circ}, x = 36 0^{\circ}

sec (x) - 3 = 0, 0 \leq x \leq 36 0^{\circ} : x = arcsec (3), x = 36 0^{\circ} - arcsec (3)

sec (x) - 3 = 0, 0 \leq x \leq 36 0^{\circ}

Verschiebe

3

auf die rechte Seite

sec (x) - 3 = 0

Füge

3

zu beiden Seiten hinzu

sec (x) - 3 + 3 = 0 + 3

Vereinfache

sec (x) = 3

sec (x) = 3

Wende die Eigenschaften der Trigonometrie an

sec (x) = 3

Allgemeine Lösung für

sec (x) = 3

sec (x) = a \Rightarrow x = arcsec (a) + 36 0^{\circ} n, x = 36 0^{\circ} - arcsec (a) + 36 0^{\circ} n

x = arcsec (3) + 36 0^{\circ} n, x = 36 0^{\circ} - arcsec (3) + 36 0^{\circ} n

x = arcsec (3) + 36 0^{\circ} n, x = 36 0^{\circ} - arcsec (3) + 36 0^{\circ} n

Lösungen für den Bereich

0 \leq x \leq 36 0^{\circ}

x = arcsec (3), x = 36 0^{\circ} - arcsec (3)

Kombiniere alle Lösungen

x = 0, x = 18 0^{\circ}, x = 36 0^{\circ}, x = arcsec (3), x = 36 0^{\circ} - arcsec (3)

Zeige Lösungen in Dezimalform

x = 0, x = 18 0^{\circ}, x = 36 0^{\circ}, x = 1.23095 \dots, x = 36 0^{\circ} - 1.23095 \dots

4 sin (\frac{x}{2}) - 1 = 1

3 sec (θ) + 6 = 0

sin (x) - sin (x) \cdot cos (x) = 0, 0 \leq x \leq 2 π

8 sin (x) + 6 cos (x) = 8

2 tan^{2} (x) - 5 tan (x) + 3 = 0