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Popular Trigonometria >

0.5=cos(pi/6 x)

Solução

0.5 = cos (\frac{π}{6} x)

Solução

x = 2 + 12 n, x = 10 + 12 n

Graus

x = 114.59155 \dots^{\circ} + 687.54935 \dots^{\circ} n, x = 572.95779 \dots^{\circ} + 687.54935 \dots^{\circ} n

Passos da solução

0.5 = cos (\frac{π}{6} x)

Trocar lados

cos (\frac{π}{6} x) = 0.5

Soluções gerais para

cos (\frac{π}{6} x) = 0.5

cos (x)

tabela de periodicidade com ciclo de

2 πn

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}{6} x = \frac{π}{3} + 2 πn, \frac{π}{6} x = \frac{5 π}{3} + 2 πn

\frac{π}{6} x = \frac{π}{3} + 2 πn, \frac{π}{6} x = \frac{5 π}{3} + 2 πn

Resolver

\frac{π}{6} x = \frac{π}{3} + 2 πn : x = 2 + 12 n

\frac{π}{6} x = \frac{π}{3} + 2 πn

Multiplicar ambos os lados por

6

\frac{π}{6} x = \frac{π}{3} + 2 πn

Multiplicar ambos os lados por

6

6 \cdot \frac{π}{6} x = 6 \cdot \frac{π}{3} + 6 \cdot 2 πn

Simplificar

6 \cdot \frac{π}{6} x = 6 \cdot \frac{π}{3} + 6 \cdot 2 πn

Simplificar

6 \cdot \frac{π}{6} x : π x

6 \cdot \frac{π}{6} x

Multiplicar frações:

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

= \frac{6 π}{6} x

Eliminar o fator comum:

6

= x π

Simplificar

6 \cdot \frac{π}{3} + 6 \cdot 2 πn : 2 π + 12 πn

6 \cdot \frac{π}{3} + 6 \cdot 2 πn

6 \cdot \frac{π}{3} = 2 π

6 \cdot \frac{π}{3}

Multiplicar frações:

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

= \frac{π 6}{3}

Dividir:

\frac{6}{3} = 2

= 2 π

6 \cdot 2 πn = 12 πn

6 \cdot 2 πn

Multiplicar os números:

6 \cdot 2 = 12

= 12 πn

= 2 π + 12 πn

π x = 2 π + 12 πn

π x = 2 π + 12 πn

π x = 2 π + 12 πn

Dividir ambos os lados por

π

π x = 2 π + 12 πn

Dividir ambos os lados por

π

\frac{π x}{π} = \frac{2 π}{π} + \frac{12 πn}{π}

Simplificar

\frac{π x}{π} = \frac{2 π}{π} + \frac{12 πn}{π}

Simplificar

\frac{π x}{π} : x

\frac{π x}{π}

Eliminar o fator comum:

π

= x

Simplificar

\frac{2 π}{π} + \frac{12 πn}{π} : 2 + 12 n

\frac{2 π}{π} + \frac{12 πn}{π}

Cancelar

\frac{2 π}{π} : 2

\frac{2 π}{π}

Eliminar o fator comum:

π

= 2

= 2 + \frac{12 πn}{π}

Cancelar

\frac{12 πn}{π} : 12 n

\frac{12 πn}{π}

Eliminar o fator comum:

π

= 12 n

= 2 + 12 n

x = 2 + 12 n

x = 2 + 12 n

x = 2 + 12 n

Resolver

\frac{π}{6} x = \frac{5 π}{3} + 2 πn : x = 10 + 12 n

\frac{π}{6} x = \frac{5 π}{3} + 2 πn

Multiplicar ambos os lados por

6

\frac{π}{6} x = \frac{5 π}{3} + 2 πn

Multiplicar ambos os lados por

6

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

Simplificar

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

Simplificar

6 \cdot \frac{π}{6} x : π x

6 \cdot \frac{π}{6} x

Multiplicar frações:

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

= \frac{6 π}{6} x

Eliminar o fator comum:

6

= x π

Simplificar

6 \cdot \frac{5 π}{3} + 6 \cdot 2 πn : 10 π + 12 πn

6 \cdot \frac{5 π}{3} + 6 \cdot 2 πn

6 \cdot \frac{5 π}{3} = 10 π

6 \cdot \frac{5 π}{3}

Multiplicar frações:

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

= \frac{5 π 6}{3}

Multiplicar os números:

5 \cdot 6 = 30

= \frac{30 π}{3}

Dividir:

\frac{30}{3} = 10

= 10 π

6 \cdot 2 πn = 12 πn

6 \cdot 2 πn

Multiplicar os números:

6 \cdot 2 = 12

= 12 πn

= 10 π + 12 πn

π x = 10 π + 12 πn

π x = 10 π + 12 πn

π x = 10 π + 12 πn

Dividir ambos os lados por

π

π x = 10 π + 12 πn

Dividir ambos os lados por

π

\frac{π x}{π} = \frac{10 π}{π} + \frac{12 πn}{π}

Simplificar

\frac{π x}{π} = \frac{10 π}{π} + \frac{12 πn}{π}

Simplificar

\frac{π x}{π} : x

\frac{π x}{π}

Eliminar o fator comum:

π

= x

Simplificar

\frac{10 π}{π} + \frac{12 πn}{π} : 10 + 12 n

\frac{10 π}{π} + \frac{12 πn}{π}

Cancelar

\frac{10 π}{π} : 10

\frac{10 π}{π}

Eliminar o fator comum:

π

= 10

= 10 + \frac{12 πn}{π}

Cancelar

\frac{12 πn}{π} : 12 n

\frac{12 πn}{π}

Eliminar o fator comum:

π

= 12 n

= 10 + 12 n

x = 10 + 12 n

x = 10 + 12 n

x = 10 + 12 n

x = 2 + 12 n, x = 10 + 12 n

Gráfico

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