de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Trigonometrie >

cos(x)>0.5

Lösung

cos (x) > 0.5

Lösung

- \frac{π}{3} + 2 πn < x < \frac{π}{3} + 2 πn

+2

Intervall-Notation

(- \frac{π}{3} + 2 πn, \frac{π}{3} + 2 πn)

Dezimale

- 1.04719 \dots + 2 πn < x < 1.04719 \dots + 2 πn

Schritte zur Lösung

cos (x) > 0.5

Für

cos (x) > a

, wenn

- 1 \leq a < 1

dann

- arccos (a) + 2 πn < x < arccos (a) + 2 πn

- arccos (0.5) + 2 πn < x < arccos (0.5) + 2 πn

Vereinfache

- arccos (0.5) : - \frac{π}{3}

- arccos (0.5)

arccos (0.5) = \frac{π}{3}

arccos (0.5)

= arccos (\frac{1}{2})

Verwende die folgende triviale Identität:

arccos (\frac{1}{2}) = \frac{π}{3}

arccos (\frac{1}{2})

x - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 arccos (x) π \frac{5 π}{6} \frac{3 π}{4} \frac{2 π}{3} \frac{π}{2} \frac{π}{3} \frac{π}{4} \frac{π}{6} 0 arccos (x) 18 0^{\circ} 15 0^{\circ} 13 5^{\circ} 12 0^{\circ} 9 0^{\circ} 6 0^{\circ} 4 5^{\circ} 3 0^{\circ} 0^{\circ}

= \frac{π}{3}

= \frac{π}{3}

= - \frac{π}{3}

Vereinfache

arccos (0.5) : \frac{π}{3}

arccos (0.5)

= arccos (\frac{1}{2})

Verwende die folgende triviale Identität:

arccos (\frac{1}{2}) = \frac{π}{3}

arccos (\frac{1}{2})

x - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 arccos (x) π \frac{5 π}{6} \frac{3 π}{4} \frac{2 π}{3} \frac{π}{2} \frac{π}{3} \frac{π}{4} \frac{π}{6} 0 arccos (x) 18 0^{\circ} 15 0^{\circ} 13 5^{\circ} 12 0^{\circ} 9 0^{\circ} 6 0^{\circ} 4 5^{\circ} 3 0^{\circ} 0^{\circ}

= \frac{π}{3}

= \frac{π}{3}

- \frac{π}{3} + 2 πn < x < \frac{π}{3} + 2 πn

Beliebte Beispiele

cos (x) < 1

sin (2 x) \geq 0

cos(x)<= sin(2x)

cos (x) \leq sin (2 x)

cos (x) < \frac{1}{2}

cos (x) < sin (x)