de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Trigonometrie >

sin^2(x)=sin^2(x)sec(x)

Lösung

sin^{2} (x) = sin^{2} (x) sec (x)

Lösung

x = 2 πn, x = π + 2 πn

+1

Grad

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

Schritte zur Lösung

sin^{2} (x) = sin^{2} (x) sec (x)

Subtrahiere

sin^{2} (x) sec (x)

von beiden Seiten

sin^{2} (x) - sin^{2} (x) sec (x) = 0

Faktorisiere

sin^{2} (x) - sin^{2} (x) sec (x) : - sin^{2} (x) (sec (x) - 1)

sin^{2} (x) - sin^{2} (x) sec (x)

Klammere gleiche Terme aus

- sin^{2} (x)

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

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

Löse jeden Teil einzeln

sin^{2} (x) = 0 or sec (x) - 1 = 0

sin^{2} (x) = 0 : x = 2 πn, x = π + 2 πn

sin^{2} (x) = 0

Wende Regel an

x^{n} = 0 \Rightarrow x = 0

sin (x) = 0

Allgemeine Lösung für

sin (x) = 0

sin (x)

Periodizitätstabelle mit

2 πn

Zyklus:

x = 0 + 2 πn, x = π + 2 πn

x = 0 + 2 πn, x = π + 2 πn

Löse

x = 0 + 2 πn : x = 2 πn

x = 0 + 2 πn

0 + 2 πn = 2 πn

x = 2 πn

x = 2 πn, x = π + 2 πn

sec (x) - 1 = 0 : x = 2 πn

sec (x) - 1 = 0

Verschiebe

1

auf die rechte Seite

sec (x) - 1 = 0

Füge

1

zu beiden Seiten hinzu

sec (x) - 1 + 1 = 0 + 1

Vereinfache

sec (x) = 1

sec (x) = 1

Allgemeine Lösung für

sec (x) = 1

sec (x)

Periodizitätstabelle mit

2 πn

Zyklus:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sec (x) 1 \frac{2 3}{3} 22 Undefined - 2 - 2 - \frac{2 3}{3} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sec (x) - 1 - \frac{2 3}{3} - 2 - 2 Undefined 22 \frac{2 3}{3}

x = 0 + 2 πn

x = 0 + 2 πn

Löse

x = 0 + 2 πn : x = 2 πn

x = 0 + 2 πn

0 + 2 πn = 2 πn

x = 2 πn

x = 2 πn

Kombiniere alle Lösungen

x = 2 πn, x = π + 2 πn

Graph

Beliebte Beispiele

sin(x)=(4.2)/(9.5)

sin (x) = \frac{4.2}{9.5}

cos(x)=(4.6)/(8.6)

cos (x) = \frac{4.6}{8.6}

5tan(x)+5tan^2(x)=0

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

8sec^2(x)-8sec(x)=16

8 sec^{2} (x) - 8 sec (x) = 16

50=36sin((2pi)/(365)(t-101))+14

50 = 36 sin (\frac{2 π}{365} (t - 101)) + 14