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Popular Trigonometria >

10=14+8sin((pit)/(12))

Solução

10 = 14 + 8 sin (\frac{π t}{12})

Solução

t = 14 + 24 n, t = 22 + 24 n

Graus

t = 802.14091 \dots^{\circ} + 1375.09870 \dots^{\circ} n, t = 1260.50714 \dots^{\circ} + 1375.09870 \dots^{\circ} n

Passos da solução

10 = 14 + 8 sin (\frac{π t}{12})

Trocar lados

14 + 8 sin (\frac{π t}{12}) = 10

Mova

14

para o lado direito

14 + 8 sin (\frac{π t}{12}) = 10

Subtrair

14

de ambos os lados

14 + 8 sin (\frac{π t}{12}) - 14 = 10 - 14

Simplificar

8 sin (\frac{π t}{12}) = - 4

8 sin (\frac{π t}{12}) = - 4

Dividir ambos os lados por

8

8 sin (\frac{π t}{12}) = - 4

Dividir ambos os lados por

8

\frac{8 sin ( \frac{π t}{12} )}{8} = \frac{- 4}{8}

Simplificar

\frac{8 sin ( \frac{π t}{12} )}{8} = \frac{- 4}{8}

Simplificar

\frac{8 sin ( \frac{π t}{12} )}{8} : sin (\frac{π t}{12})

\frac{8 sin ( \frac{π t}{12} )}{8}

Dividir:

\frac{8}{8} = 1

= sin (\frac{π t}{12})

Simplificar

\frac{- 4}{8} : - \frac{1}{2}

\frac{- 4}{8}

Aplicar as propriedades das frações:

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

= - \frac{4}{8}

Eliminar o fator comum:

4

= - \frac{1}{2}

sin (\frac{π t}{12}) = - \frac{1}{2}

sin (\frac{π t}{12}) = - \frac{1}{2}

sin (\frac{π t}{12}) = - \frac{1}{2}

Soluções gerais para

sin (\frac{π t}{12}) = - \frac{1}{2}

sin (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} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{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} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

\frac{π t}{12} = \frac{7 π}{6} + 2 πn, \frac{π t}{12} = \frac{11 π}{6} + 2 πn

\frac{π t}{12} = \frac{7 π}{6} + 2 πn, \frac{π t}{12} = \frac{11 π}{6} + 2 πn

Resolver

\frac{π t}{12} = \frac{7 π}{6} + 2 πn : t = 14 + 24 n

\frac{π t}{12} = \frac{7 π}{6} + 2 πn

Multiplicar ambos os lados por

12

\frac{π t}{12} = \frac{7 π}{6} + 2 πn

Multiplicar ambos os lados por

12

\frac{12 π t}{12} = 12 \cdot \frac{7 π}{6} + 12 \cdot 2 πn

Simplificar

\frac{12 π t}{12} = 12 \cdot \frac{7 π}{6} + 12 \cdot 2 πn

Simplificar

\frac{12 π t}{12} : π t

\frac{12 π t}{12}

Dividir:

\frac{12}{12} = 1

= π t

Simplificar

12 \cdot \frac{7 π}{6} + 12 \cdot 2 πn : 14 π + 24 πn

12 \cdot \frac{7 π}{6} + 12 \cdot 2 πn

12 \cdot \frac{7 π}{6} = 14 π

12 \cdot \frac{7 π}{6}

Multiplicar frações:

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

= \frac{7 π 12}{6}

Multiplicar os números:

7 \cdot 12 = 84

= \frac{84 π}{6}

Dividir:

\frac{84}{6} = 14

= 14 π

12 \cdot 2 πn = 24 πn

12 \cdot 2 πn

Multiplicar os números:

12 \cdot 2 = 24

= 24 πn

= 14 π + 24 πn

π t = 14 π + 24 πn

π t = 14 π + 24 πn

π t = 14 π + 24 πn

Dividir ambos os lados por

π

π t = 14 π + 24 πn

Dividir ambos os lados por

π

\frac{π t}{π} = \frac{14 π}{π} + \frac{24 πn}{π}

Simplificar

\frac{π t}{π} = \frac{14 π}{π} + \frac{24 πn}{π}

Simplificar

\frac{π t}{π} : t

\frac{π t}{π}

Eliminar o fator comum:

π

= t

Simplificar

\frac{14 π}{π} + \frac{24 πn}{π} : 14 + 24 n

\frac{14 π}{π} + \frac{24 πn}{π}

Cancelar

\frac{14 π}{π} : 14

\frac{14 π}{π}

Eliminar o fator comum:

π

= 14

= 14 + \frac{24 πn}{π}

Cancelar

\frac{24 πn}{π} : 24 n

\frac{24 πn}{π}

Eliminar o fator comum:

π

= 24 n

= 14 + 24 n

t = 14 + 24 n

t = 14 + 24 n

t = 14 + 24 n

Resolver

\frac{π t}{12} = \frac{11 π}{6} + 2 πn : t = 22 + 24 n

\frac{π t}{12} = \frac{11 π}{6} + 2 πn

Multiplicar ambos os lados por

12

\frac{π t}{12} = \frac{11 π}{6} + 2 πn

Multiplicar ambos os lados por

12

\frac{12 π t}{12} = 12 \cdot \frac{11 π}{6} + 12 \cdot 2 πn

Simplificar

\frac{12 π t}{12} = 12 \cdot \frac{11 π}{6} + 12 \cdot 2 πn

Simplificar

\frac{12 π t}{12} : π t

\frac{12 π t}{12}

Dividir:

\frac{12}{12} = 1

= π t

Simplificar

12 \cdot \frac{11 π}{6} + 12 \cdot 2 πn : 22 π + 24 πn

12 \cdot \frac{11 π}{6} + 12 \cdot 2 πn

12 \cdot \frac{11 π}{6} = 22 π

12 \cdot \frac{11 π}{6}

Multiplicar frações:

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

= \frac{11 π 12}{6}

Multiplicar os números:

11 \cdot 12 = 132

= \frac{132 π}{6}

Dividir:

\frac{132}{6} = 22

= 22 π

12 \cdot 2 πn = 24 πn

12 \cdot 2 πn

Multiplicar os números:

12 \cdot 2 = 24

= 24 πn

= 22 π + 24 πn

π t = 22 π + 24 πn

π t = 22 π + 24 πn

π t = 22 π + 24 πn

Dividir ambos os lados por

π

π t = 22 π + 24 πn

Dividir ambos os lados por

π

\frac{π t}{π} = \frac{22 π}{π} + \frac{24 πn}{π}

Simplificar

\frac{π t}{π} = \frac{22 π}{π} + \frac{24 πn}{π}

Simplificar

\frac{π t}{π} : t

\frac{π t}{π}

Eliminar o fator comum:

π

= t

Simplificar

\frac{22 π}{π} + \frac{24 πn}{π} : 22 + 24 n

\frac{22 π}{π} + \frac{24 πn}{π}

Cancelar

\frac{22 π}{π} : 22

\frac{22 π}{π}

Eliminar o fator comum:

π

= 22

= 22 + \frac{24 πn}{π}

Cancelar

\frac{24 πn}{π} : 24 n

\frac{24 πn}{π}

Eliminar o fator comum:

π

= 24 n

= 22 + 24 n

t = 22 + 24 n

t = 22 + 24 n

t = 22 + 24 n

t = 14 + 24 n, t = 22 + 24 n

Gráfico

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