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cos((pi(x+5))/3)= 1/2

Solución

cos (\frac{π ( x + 5 )}{3}) = \frac{1}{2}

Solución

x = 6 n - 4, x = 6 n

Grados

x = - 229.18311 \dots^{\circ} + 343.77467 \dots^{\circ} n, x = 0^{\circ} + 343.77467 \dots^{\circ} n

Pasos de solución

cos (\frac{π ( x + 5 )}{3}) = \frac{1}{2}

Soluciones generales para

cos (\frac{π ( x + 5 )}{3}) = \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}

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

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

Resolver

\frac{π ( x + 5 )}{3} = \frac{π}{3} + 2 πn : x = 6 n - 4

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

Multiplicar ambos lados por

3

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

Multiplicar ambos lados por

3

\frac{3 π ( x + 5 )}{3} = 3 \cdot \frac{π}{3} + 3 \cdot 2 πn

Simplificar

\frac{3 π ( x + 5 )}{3} = 3 \cdot \frac{π}{3} + 3 \cdot 2 πn

Simplificar

\frac{3 π ( x + 5 )}{3} : π (x + 5)

\frac{3 π ( x + 5 )}{3}

Dividir:

\frac{3}{3} = 1

= π (x + 5)

Simplificar

3 \cdot \frac{π}{3} + 3 \cdot 2 πn : π + 6 πn

3 \cdot \frac{π}{3} + 3 \cdot 2 πn

3 \cdot \frac{π}{3} = π

3 \cdot \frac{π}{3}

Multiplicar fracciones:

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

= \frac{π 3}{3}

Eliminar los terminos comunes:

3

= π

3 \cdot 2 πn = 6 πn

3 \cdot 2 πn

Multiplicar los numeros:

3 \cdot 2 = 6

= 6 πn

= π + 6 πn

π (x + 5) = π + 6 πn

π (x + 5) = π + 6 πn

π (x + 5) = π + 6 πn

Dividir ambos lados entre

π

π (x + 5) = π + 6 πn

Dividir ambos lados entre

π

\frac{π ( x + 5 )}{π} = \frac{π}{π} + \frac{6 πn}{π}

Simplificar

\frac{π ( x + 5 )}{π} = \frac{π}{π} + \frac{6 πn}{π}

Simplificar

\frac{π ( x + 5 )}{π} : x + 5

\frac{π ( x + 5 )}{π}

Eliminar los terminos comunes:

π

= x + 5

Simplificar

\frac{π}{π} + \frac{6 πn}{π} : 1 + 6 n

\frac{π}{π} + \frac{6 πn}{π}

Aplicar la regla

\frac{a}{a} = 1

\frac{π}{π} = 1

= 1 + \frac{6 πn}{π}

Cancelar

\frac{6 πn}{π} : 6 n

\frac{6 πn}{π}

Eliminar los terminos comunes:

π

= 6 n

= 1 + 6 n

x + 5 = 1 + 6 n

x + 5 = 1 + 6 n

x + 5 = 1 + 6 n

Mover

5

al lado derecho

x + 5 = 1 + 6 n

Restar

5

de ambos lados

x + 5 - 5 = 1 + 6 n - 5

Simplificar

x = 6 n - 4

x = 6 n - 4

Resolver

\frac{π ( x + 5 )}{3} = \frac{5 π}{3} + 2 πn : x = 6 n

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

Multiplicar ambos lados por

3

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

Multiplicar ambos lados por

3

\frac{3 π ( x + 5 )}{3} = 3 \cdot \frac{5 π}{3} + 3 \cdot 2 πn

Simplificar

\frac{3 π ( x + 5 )}{3} = 3 \cdot \frac{5 π}{3} + 3 \cdot 2 πn

Simplificar

\frac{3 π ( x + 5 )}{3} : π (x + 5)

\frac{3 π ( x + 5 )}{3}

Dividir:

\frac{3}{3} = 1

= π (x + 5)

Simplificar

3 \cdot \frac{5 π}{3} + 3 \cdot 2 πn : 5 π + 6 πn

3 \cdot \frac{5 π}{3} + 3 \cdot 2 πn

3 \cdot \frac{5 π}{3} = 5 π

3 \cdot \frac{5 π}{3}

Multiplicar fracciones:

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

= \frac{5 π 3}{3}

Eliminar los terminos comunes:

3

= 5 π

3 \cdot 2 πn = 6 πn

3 \cdot 2 πn

Multiplicar los numeros:

3 \cdot 2 = 6

= 6 πn

= 5 π + 6 πn

π (x + 5) = 5 π + 6 πn

π (x + 5) = 5 π + 6 πn

π (x + 5) = 5 π + 6 πn

Dividir ambos lados entre

π

π (x + 5) = 5 π + 6 πn

Dividir ambos lados entre

π

\frac{π ( x + 5 )}{π} = \frac{5 π}{π} + \frac{6 πn}{π}

Simplificar

\frac{π ( x + 5 )}{π} = \frac{5 π}{π} + \frac{6 πn}{π}

Simplificar

\frac{π ( x + 5 )}{π} : x + 5

\frac{π ( x + 5 )}{π}

Eliminar los terminos comunes:

π

= x + 5

Simplificar

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

\frac{5 π}{π} + \frac{6 πn}{π}

Cancelar

\frac{5 π}{π} : 5

\frac{5 π}{π}

Eliminar los terminos comunes:

π

= 5

= 5 + \frac{6 πn}{π}

Cancelar

\frac{6 πn}{π} : 6 n

\frac{6 πn}{π}

Eliminar los terminos comunes:

π

= 6 n

= 5 + 6 n

x + 5 = 5 + 6 n

x + 5 = 5 + 6 n

x + 5 = 5 + 6 n

Mover

5

al lado derecho

x + 5 = 5 + 6 n

Restar

5

de ambos lados

x + 5 - 5 = 5 + 6 n - 5

Simplificar

x = 6 n

x = 6 n

x = 6 n - 4, x = 6 n

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