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sqrt(2)cos(x)+1=0,pi<x<4pi

Solución

2 cos (x) + 1 = 0, π < x < 4 π

Solución

x = \frac{5 π}{4}, x = \frac{11 π}{4}, x = \frac{13 π}{4}

+1

Grados

x = 22 5^{\circ}, x = 49 5^{\circ}, x = 58 5^{\circ}

Pasos de solución

2 cos (x) + 1 = 0, π < x < 4 π

Mover

1

al lado derecho

2 cos (x) + 1 = 0

Restar

1

de ambos lados

2 cos (x) + 1 - 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

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

Simplificar

\frac{2 cos ( x )}{2} : cos (x)

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

Eliminar los terminos comunes:

2

= cos (x)

Simplificar

\frac{- 1}{2} : - \frac{2}{2}

\frac{- 1}{2}

Aplicar las propiedades de las fracciones:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{1}{2}

Racionalizar

- \frac{1}{2} : - \frac{2}{2}

- \frac{1}{2}

Multiplicar por el conjugado

\frac{2}{2}

= - \frac{1 \cdot 2}{2 2}

1 \cdot 2 = 2

22 = 2

22

Aplicar las leyes de los exponentes:

a a = a

22 = 2

= 2

= - \frac{2}{2}

= - \frac{2}{2}

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

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

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

Soluciones generales para

cos (x) = - \frac{2}{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{3 π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn

x = \frac{3 π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn

Soluciones para el rango

π < x < 4 π

x = \frac{5 π}{4}, x = \frac{11 π}{4}, x = \frac{13 π}{4}

Ejemplos populares

cos (3 x) = 3

4cos^2(θ)-5cos(θ)=-4cos(θ)+3

4 cos^{2} (θ) - 5 cos (θ) = - 4 cos (θ) + 3

solvefor x,cos(x)=-0.5 resolver para

x, cos (x) = - 0.5

-2cos(x)=3sin(x)

- 2 cos (x) = 3 sin (x)

3sin(x)-cos(2x)=1

3 sin (x) - cos (2 x) = 1