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2cos(pi/5 x)=sqrt(3)

Solución

2 cos (\frac{π}{5} x) = 3

Solución

x = \frac{5}{6} + 10 n, x = \frac{55}{6} + 10 n

Grados

x = 47.74648 \dots^{\circ} + 572.95779 \dots^{\circ} n, x = 525.21131 \dots^{\circ} + 572.95779 \dots^{\circ} n

Pasos de solución

2 cos (\frac{π}{5} x) = 3

Dividir ambos lados entre

2

2 cos (\frac{π}{5} x) = 3

Dividir ambos lados entre

2

\frac{2 cos ( \frac{π}{5} x )}{2} = \frac{3}{2}

Simplificar

cos (\frac{π}{5} x) = \frac{3}{2}

cos (\frac{π}{5} x) = \frac{3}{2}

Soluciones generales para

cos (\frac{π}{5} x) = \frac{3}{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}

\frac{π}{5} x = \frac{π}{6} + 2 πn, \frac{π}{5} x = \frac{11 π}{6} + 2 πn

\frac{π}{5} x = \frac{π}{6} + 2 πn, \frac{π}{5} x = \frac{11 π}{6} + 2 πn

Resolver

\frac{π}{5} x = \frac{π}{6} + 2 πn : x = \frac{5}{6} + 10 n

\frac{π}{5} x = \frac{π}{6} + 2 πn

Multiplicar ambos lados por

5

\frac{π}{5} x = \frac{π}{6} + 2 πn

Multiplicar ambos lados por

5

5 \cdot \frac{π}{5} x = 5 \cdot \frac{π}{6} + 5 \cdot 2 πn

Simplificar

5 \cdot \frac{π}{5} x = 5 \cdot \frac{π}{6} + 5 \cdot 2 πn

Simplificar

5 \cdot \frac{π}{5} x : π x

5 \cdot \frac{π}{5} x

Multiplicar fracciones:

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

= \frac{5 π}{5} x

Eliminar los terminos comunes:

5

= x π

Simplificar

5 \cdot \frac{π}{6} + 5 \cdot 2 πn : \frac{5 π}{6} + 10 πn

5 \cdot \frac{π}{6} + 5 \cdot 2 πn

Multiplicar

5 \cdot \frac{π}{6} : \frac{5 π}{6}

5 \cdot \frac{π}{6}

Multiplicar fracciones:

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

= \frac{π 5}{6}

= \frac{5 π}{6} + 5 \cdot 2 πn

Multiplicar los numeros:

5 \cdot 2 = 10

= \frac{5 π}{6} + 10 πn

π x = \frac{5 π}{6} + 10 πn

π x = \frac{5 π}{6} + 10 πn

π x = \frac{5 π}{6} + 10 πn

Dividir ambos lados entre

π

π x = \frac{5 π}{6} + 10 πn

Dividir ambos lados entre

π

\frac{π x}{π} = \frac{\frac{5 π}{6}}{π} + \frac{10 πn}{π}

Simplificar

\frac{π x}{π} = \frac{\frac{5 π}{6}}{π} + \frac{10 πn}{π}

Simplificar

\frac{π x}{π} : x

\frac{π x}{π}

Eliminar los terminos comunes:

π

= x

Simplificar

\frac{\frac{5 π}{6}}{π} + \frac{10 πn}{π} : \frac{5}{6} + 10 n

\frac{\frac{5 π}{6}}{π} + \frac{10 πn}{π}

\frac{\frac{5 π}{6}}{π} = \frac{5}{6}

\frac{\frac{5 π}{6}}{π}

Aplicar las propiedades de las fracciones:

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

= \frac{5 π}{6 π}

Eliminar los terminos comunes:

π

= \frac{5}{6}

\frac{10 πn}{π} = 10 n

\frac{10 πn}{π}

Eliminar los terminos comunes:

π

= 10 n

= \frac{5}{6} + 10 n

x = \frac{5}{6} + 10 n

x = \frac{5}{6} + 10 n

x = \frac{5}{6} + 10 n

Resolver

\frac{π}{5} x = \frac{11 π}{6} + 2 πn : x = \frac{55}{6} + 10 n

\frac{π}{5} x = \frac{11 π}{6} + 2 πn

Multiplicar ambos lados por

5

\frac{π}{5} x = \frac{11 π}{6} + 2 πn

Multiplicar ambos lados por

5

5 \cdot \frac{π}{5} x = 5 \cdot \frac{11 π}{6} + 5 \cdot 2 πn

Simplificar

5 \cdot \frac{π}{5} x = 5 \cdot \frac{11 π}{6} + 5 \cdot 2 πn

Simplificar

5 \cdot \frac{π}{5} x : π x

5 \cdot \frac{π}{5} x

Multiplicar fracciones:

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

= \frac{5 π}{5} x

Eliminar los terminos comunes:

5

= x π

Simplificar

5 \cdot \frac{11 π}{6} + 5 \cdot 2 πn : \frac{55 π}{6} + 10 πn

5 \cdot \frac{11 π}{6} + 5 \cdot 2 πn

5 \cdot \frac{11 π}{6} = \frac{55 π}{6}

5 \cdot \frac{11 π}{6}

Multiplicar fracciones:

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

= \frac{11 π 5}{6}

Multiplicar los numeros:

11 \cdot 5 = 55

= \frac{55 π}{6}

5 \cdot 2 πn = 10 πn

5 \cdot 2 πn

Multiplicar los numeros:

5 \cdot 2 = 10

= 10 πn

= \frac{55 π}{6} + 10 πn

π x = \frac{55 π}{6} + 10 πn

π x = \frac{55 π}{6} + 10 πn

π x = \frac{55 π}{6} + 10 πn

Dividir ambos lados entre

π

π x = \frac{55 π}{6} + 10 πn

Dividir ambos lados entre

π

\frac{π x}{π} = \frac{\frac{55 π}{6}}{π} + \frac{10 πn}{π}

Simplificar

\frac{π x}{π} = \frac{\frac{55 π}{6}}{π} + \frac{10 πn}{π}

Simplificar

\frac{π x}{π} : x

\frac{π x}{π}

Eliminar los terminos comunes:

π

= x

Simplificar

\frac{\frac{55 π}{6}}{π} + \frac{10 πn}{π} : \frac{55}{6} + 10 n

\frac{\frac{55 π}{6}}{π} + \frac{10 πn}{π}

\frac{\frac{55 π}{6}}{π} = \frac{55}{6}

\frac{\frac{55 π}{6}}{π}

Aplicar las propiedades de las fracciones:

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

= \frac{55 π}{6 π}

Eliminar los terminos comunes:

π

= \frac{55}{6}

\frac{10 πn}{π} = 10 n

\frac{10 πn}{π}

Eliminar los terminos comunes:

π

= 10 n

= \frac{55}{6} + 10 n

x = \frac{55}{6} + 10 n

x = \frac{55}{6} + 10 n

x = \frac{55}{6} + 10 n

x = \frac{5}{6} + 10 n, x = \frac{55}{6} + 10 n

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