de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Trigonometrie >

5cos^2(x)+3cos(x)-1=0

Lösung

5 cos^{2} (x) + 3 cos (x) - 1 = 0

Lösung

x = 1.32995 \dots + 2 πn, x = 2 π - 1.32995 \dots + 2 πn, x = 2.56535 \dots + 2 πn, x = - 2.56535 \dots + 2 πn

+1

Grad

x = 76.20100 \dots^{\circ} + 36 0^{\circ} n, x = 283.79899 \dots^{\circ} + 36 0^{\circ} n, x = 146.98379 \dots^{\circ} + 36 0^{\circ} n, x = - 146.98379 \dots^{\circ} + 36 0^{\circ} n

Schritte zur Lösung

5 cos^{2} (x) + 3 cos (x) - 1 = 0

Löse mit Substitution

5 cos^{2} (x) + 3 cos (x) - 1 = 0

Angenommen:

cos (x) = u

5 u^{2} + 3 u - 1 = 0

5 u^{2} + 3 u - 1 = 0 : u = \frac{- 3 + 29}{10}, u = \frac{- 3 - 29}{10}

5 u^{2} + 3 u - 1 = 0

Löse mit der quadratischen Formel

5 u^{2} + 3 u - 1 = 0

Quadratische Formel für Gliechungen:

Für

a = 5, b = 3, c = - 1

u_{1, 2} = \frac{- 3 \pm 3 ^{2} - 4 \cdot 5 ( - 1 )}{2 \cdot 5}

u_{1, 2} = \frac{- 3 \pm 3 ^{2} - 4 \cdot 5 ( - 1 )}{2 \cdot 5}

3^{2} - 4 \cdot 5 (- 1) = 29

3^{2} - 4 \cdot 5 (- 1)

Wende Regel an

- (- a) = a

= 3^{2} + 4 \cdot 5 \cdot 1

Multipliziere die Zahlen:

4 \cdot 5 \cdot 1 = 20

= 3^{2} + 20

3^{2} = 9

= 9 + 20

Addiere die Zahlen:

9 + 20 = 29

= 29

u_{1, 2} = \frac{- 3 \pm 29}{2 \cdot 5}

Trenne die Lösungen

u_{1} = \frac{- 3 + 29}{2 \cdot 5}, u_{2} = \frac{- 3 - 29}{2 \cdot 5}

u = \frac{- 3 + 29}{2 \cdot 5} : \frac{- 3 + 29}{10}

\frac{- 3 + 29}{2 \cdot 5}

Multipliziere die Zahlen:

2 \cdot 5 = 10

= \frac{- 3 + 29}{10}

u = \frac{- 3 - 29}{2 \cdot 5} : \frac{- 3 - 29}{10}

\frac{- 3 - 29}{2 \cdot 5}

Multipliziere die Zahlen:

2 \cdot 5 = 10

= \frac{- 3 - 29}{10}

Die Lösungen für die quadratische Gleichung sind:

u = \frac{- 3 + 29}{10}, u = \frac{- 3 - 29}{10}

Setze in

u = cos (x)

ein

cos (x) = \frac{- 3 + 29}{10}, cos (x) = \frac{- 3 - 29}{10}

cos (x) = \frac{- 3 + 29}{10}, cos (x) = \frac{- 3 - 29}{10}

cos (x) = \frac{- 3 + 29}{10} : x = arccos (\frac{- 3 + 29}{10}) + 2 πn, x = 2 π - arccos (\frac{- 3 + 29}{10}) + 2 πn

cos (x) = \frac{- 3 + 29}{10}

Wende die Eigenschaften der Trigonometrie an

cos (x) = \frac{- 3 + 29}{10}

Allgemeine Lösung für

cos (x) = \frac{- 3 + 29}{10}

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = 2 π - arccos (a) + 2 πn

x = arccos (\frac{- 3 + 29}{10}) + 2 πn, x = 2 π - arccos (\frac{- 3 + 29}{10}) + 2 πn

x = arccos (\frac{- 3 + 29}{10}) + 2 πn, x = 2 π - arccos (\frac{- 3 + 29}{10}) + 2 πn

cos (x) = \frac{- 3 - 29}{10} : x = arccos (\frac{- 3 - 29}{10}) + 2 πn, x = - arccos (\frac{- 3 - 29}{10}) + 2 πn

cos (x) = \frac{- 3 - 29}{10}

Wende die Eigenschaften der Trigonometrie an

cos (x) = \frac{- 3 - 29}{10}

Allgemeine Lösung für

cos (x) = \frac{- 3 - 29}{10}

cos (x) = - a \Rightarrow x = arccos (- a) + 2 πn, x = - arccos (- a) + 2 πn

x = arccos (\frac{- 3 - 29}{10}) + 2 πn, x = - arccos (\frac{- 3 - 29}{10}) + 2 πn

x = arccos (\frac{- 3 - 29}{10}) + 2 πn, x = - arccos (\frac{- 3 - 29}{10}) + 2 πn

Kombiniere alle Lösungen

x = arccos (\frac{- 3 + 29}{10}) + 2 πn, x = 2 π - arccos (\frac{- 3 + 29}{10}) + 2 πn, x = arccos (\frac{- 3 - 29}{10}) + 2 πn, x = - arccos (\frac{- 3 - 29}{10}) + 2 πn

Zeige Lösungen in Dezimalform

x = 1.32995 \dots + 2 πn, x = 2 π - 1.32995 \dots + 2 πn, x = 2.56535 \dots + 2 πn, x = - 2.56535 \dots + 2 πn

Graph

Beliebte Beispiele

3 cot (x) + 5 = 8

solvefor a,sin(arccos(x))=sqrt(1-x^2)

so l v e f or a, sin (arccos (x)) = 1 - x^{2}

7 cos (5 x) = 6

3sin(x)=3tan(x)

3 sin (x) = 3 tan (x)

cos (2 a) = - 1