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2cos^2(4x+1)=0

Solución

2 cos^{2} (4 x + 1) = 0

Solución

x = - \frac{1}{4} + \frac{π}{8} + \frac{πn}{2}, x = - \frac{1}{4} + \frac{3 π}{8} + \frac{πn}{2}

Grados

x = 8.17605 \dots^{\circ} + 9 0^{\circ} n, x = 53.17605 \dots^{\circ} + 9 0^{\circ} n

Pasos de solución

2 cos^{2} (4 x + 1) = 0

Dividir ambos lados entre

2

2 cos^{2} (4 x + 1) = 0

Dividir ambos lados entre

2

2 cos^{2} (4 x + 1) = 0

Dividir ambos lados entre

2

\frac{2 cos ^{2} ( 4 x + 1 )}{2} = \frac{0}{2}

Simplificar

cos^{2} (4 x + 1) = 0

cos^{2} (4 x + 1) = 0

Aplicar la regla

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

cos (4 x + 1) = 0

Soluciones generales para

cos (4 x + 1) = 0

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}

4 x + 1 = \frac{π}{2} + 2 πn, 4 x + 1 = \frac{3 π}{2} + 2 πn

4 x + 1 = \frac{π}{2} + 2 πn, 4 x + 1 = \frac{3 π}{2} + 2 πn

Resolver

4 x + 1 = \frac{π}{2} + 2 πn : x = - \frac{1}{4} + \frac{π}{8} + \frac{πn}{2}

4 x + 1 = \frac{π}{2} + 2 πn

Mover

1

al lado derecho

4 x + 1 = \frac{π}{2} + 2 πn

Restar

1

de ambos lados

4 x + 1 - 1 = \frac{π}{2} + 2 πn - 1

Simplificar

4 x = \frac{π}{2} + 2 πn - 1

4 x = \frac{π}{2} + 2 πn - 1

Dividir ambos lados entre

4

4 x = \frac{π}{2} + 2 πn - 1

Dividir ambos lados entre

4

\frac{4 x}{4} = \frac{\frac{π}{2}}{4} + \frac{2 πn}{4} - \frac{1}{4}

Simplificar

\frac{4 x}{4} = \frac{\frac{π}{2}}{4} + \frac{2 πn}{4} - \frac{1}{4}

Simplificar

\frac{4 x}{4} : x

\frac{4 x}{4}

Dividir:

\frac{4}{4} = 1

= x

Simplificar

\frac{\frac{π}{2}}{4} + \frac{2 πn}{4} - \frac{1}{4} : - \frac{1}{4} + \frac{π}{8} + \frac{πn}{2}

\frac{\frac{π}{2}}{4} + \frac{2 πn}{4} - \frac{1}{4}

Agrupar términos semejantes

= - \frac{1}{4} + \frac{2 πn}{4} + \frac{\frac{π}{2}}{4}

\frac{2 πn}{4} = \frac{πn}{2}

\frac{2 πn}{4}

Eliminar los terminos comunes:

2

= \frac{πn}{2}

\frac{\frac{π}{2}}{4} = \frac{π}{8}

\frac{\frac{π}{2}}{4}

Aplicar las propiedades de las fracciones:

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

= \frac{π}{2 \cdot 4}

Multiplicar los numeros:

2 \cdot 4 = 8

= \frac{π}{8}

= - \frac{1}{4} + \frac{πn}{2} + \frac{π}{8}

Agrupar términos semejantes

= - \frac{1}{4} + \frac{π}{8} + \frac{πn}{2}

x = - \frac{1}{4} + \frac{π}{8} + \frac{πn}{2}

x = - \frac{1}{4} + \frac{π}{8} + \frac{πn}{2}

x = - \frac{1}{4} + \frac{π}{8} + \frac{πn}{2}

Resolver

4 x + 1 = \frac{3 π}{2} + 2 πn : x = - \frac{1}{4} + \frac{3 π}{8} + \frac{πn}{2}

4 x + 1 = \frac{3 π}{2} + 2 πn

Mover

1

al lado derecho

4 x + 1 = \frac{3 π}{2} + 2 πn

Restar

1

de ambos lados

4 x + 1 - 1 = \frac{3 π}{2} + 2 πn - 1

Simplificar

4 x = \frac{3 π}{2} + 2 πn - 1

4 x = \frac{3 π}{2} + 2 πn - 1

Dividir ambos lados entre

4

4 x = \frac{3 π}{2} + 2 πn - 1

Dividir ambos lados entre

4

\frac{4 x}{4} = \frac{\frac{3 π}{2}}{4} + \frac{2 πn}{4} - \frac{1}{4}

Simplificar

\frac{4 x}{4} = \frac{\frac{3 π}{2}}{4} + \frac{2 πn}{4} - \frac{1}{4}

Simplificar

\frac{4 x}{4} : x

\frac{4 x}{4}

Dividir:

\frac{4}{4} = 1

= x

Simplificar

\frac{\frac{3 π}{2}}{4} + \frac{2 πn}{4} - \frac{1}{4} : - \frac{1}{4} + \frac{3 π}{8} + \frac{πn}{2}

\frac{\frac{3 π}{2}}{4} + \frac{2 πn}{4} - \frac{1}{4}

Agrupar términos semejantes

= - \frac{1}{4} + \frac{2 πn}{4} + \frac{\frac{3 π}{2}}{4}

\frac{2 πn}{4} = \frac{πn}{2}

\frac{2 πn}{4}

Eliminar los terminos comunes:

2

= \frac{πn}{2}

\frac{\frac{3 π}{2}}{4} = \frac{3 π}{8}

\frac{\frac{3 π}{2}}{4}

Aplicar las propiedades de las fracciones:

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

= \frac{3 π}{2 \cdot 4}

Multiplicar los numeros:

2 \cdot 4 = 8

= \frac{3 π}{8}

= - \frac{1}{4} + \frac{πn}{2} + \frac{3 π}{8}

Agrupar términos semejantes

= - \frac{1}{4} + \frac{3 π}{8} + \frac{πn}{2}

x = - \frac{1}{4} + \frac{3 π}{8} + \frac{πn}{2}

x = - \frac{1}{4} + \frac{3 π}{8} + \frac{πn}{2}

x = - \frac{1}{4} + \frac{3 π}{8} + \frac{πn}{2}

x = - \frac{1}{4} + \frac{π}{8} + \frac{πn}{2}, x = - \frac{1}{4} + \frac{3 π}{8} + \frac{πn}{2}

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