English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

cos^3(x)+sin^2(x)*cos(x)=-1/2

Solución

cos^{3} (x) + sin^{2} (x) \cdot cos (x) = - \frac{1}{2}

Solución

x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

Grados

x = 12 0^{\circ} + 36 0^{\circ} n, x = 24 0^{\circ} + 36 0^{\circ} n

Pasos de solución

cos^{3} (x) + sin^{2} (x) cos (x) = - \frac{1}{2}

Restar

- \frac{1}{2}

de ambos lados

cos^{3} (x) + sin^{2} (x) cos (x) + \frac{1}{2} = 0

Simplificar

cos^{3} (x) + sin^{2} (x) cos (x) + \frac{1}{2} : \frac{2 cos ^{3} ( x ) + 2 sin ^{2} ( x ) cos ( x ) + 1}{2}

cos^{3} (x) + sin^{2} (x) cos (x) + \frac{1}{2}

Convertir a fracción:

cos^{3} (x) = \frac{cos ^{3} ( x ) 2}{2}, sin^{2} (x) cos (x) = \frac{sin ^{2} ( x ) cos ( x ) 2}{2}

= \frac{cos ^{3} ( x ) \cdot 2}{2} + \frac{sin ^{2} ( x ) cos ( x ) \cdot 2}{2} + \frac{1}{2}

Ya que los denominadores son iguales, combinar las fracciones:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{cos ^{3} ( x ) \cdot 2 + sin ^{2} ( x ) cos ( x ) \cdot 2 + 1}{2}

\frac{2 cos ^{3} ( x ) + 2 sin ^{2} ( x ) cos ( x ) + 1}{2} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

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

Re-escribir usando identidades trigonométricas

1 + 2 cos^{3} (x) + 2 cos (x) sin^{2} (x)

Utilizar la identidad pitagórica:

cos^{2} (x) + sin^{2} (x) = 1

sin^{2} (x) = 1 - cos^{2} (x)

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

Simplificar

1 + 2 cos^{3} (x) + 2 cos (x) (1 - cos^{2} (x)) : 2 cos (x) + 1

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

Expandir

2 cos (x) (1 - cos^{2} (x)) : 2 cos (x) - 2 cos^{3} (x)

2 cos (x) (1 - cos^{2} (x))

Poner los parentesis utilizando:

a (b - c) = ab - a c

a = 2 cos (x), b = 1, c = cos^{2} (x)

= 2 cos (x) \cdot 1 - 2 cos (x) cos^{2} (x)

= 2 \cdot 1 \cdot cos (x) - 2 cos^{2} (x) cos (x)

Simplificar

2 \cdot 1 \cdot cos (x) - 2 cos^{2} (x) cos (x) : 2 cos (x) - 2 cos^{3} (x)

2 \cdot 1 \cdot cos (x) - 2 cos^{2} (x) cos (x)

2 \cdot 1 \cdot cos (x) = 2 cos (x)

2 \cdot 1 \cdot cos (x)

Multiplicar los numeros:

2 \cdot 1 = 2

= 2 cos (x)

2 cos^{2} (x) cos (x) = 2 cos^{3} (x)

2 cos^{2} (x) cos (x)

Aplicar las leyes de los exponentes:

a^{b} \cdot a^{c} = a^{b + c}

cos^{2} (x) cos (x) = cos^{2 + 1} (x)

= 2 cos^{2 + 1} (x)

Sumar:

2 + 1 = 3

= 2 cos^{3} (x)

= 2 cos (x) - 2 cos^{3} (x)

= 2 cos (x) - 2 cos^{3} (x)

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

Simplificar

1 + 2 cos^{3} (x) + 2 cos (x) - 2 cos^{3} (x) : 2 cos (x) + 1

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

Agrupar términos semejantes

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

Sumar elementos similares:

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

= 2 cos (x) + 1

= 2 cos (x) + 1

= 2 cos (x) + 1

1 + 2 cos (x) = 0

Mover

1

al lado derecho

1 + 2 cos (x) = 0

Restar

1

de ambos lados

1 + 2 cos (x) - 1 = 0 - 1

Simplificar

2 cos (x) = - 1

2 cos (x) = - 1

Dividir ambos lados entre

2

2 cos (x) = - 1

Dividir ambos lados entre

2

\frac{2 cos ( x )}{2} = \frac{- 1}{2}

Simplificar

cos (x) = - \frac{1}{2}

cos (x) = - \frac{1}{2}

Soluciones generales para

cos (x) = - \frac{1}{2}

cos (x)

tabla de valores periódicos con

2 πn

intervalos:

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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} 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} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

Ejemplos populares

cos(3A)+sin(A)=0

cos (3 A) + sin (A) = 0

0=1-sec^2(x)

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

sin(θ)=0.1

sin (θ) = 0.1

2/(sin(x))+10=6

\frac{2}{sin ( x )} + 10 = 6

sin(θ)-0.2cos(θ)=0.6377

sin (θ) - 0.2 cos (θ) = 0.6377