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Popular Trigonometria >

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

Solução

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

Solução

x = 2 πn - \frac{π}{3}, x = 2 πn + π

Graus

x = - 6 0^{\circ} + 36 0^{\circ} n, x = 18 0^{\circ} + 36 0^{\circ} n

Passos da solução

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

Trocar lados

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

Mova

2

para o lado direito

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

Subtrair

2

de ambos os lados

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

Simplificar

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

Simplificar

2 + cos (x + \frac{2 π}{3}) - 2 : cos (x + \frac{2 π}{3})

2 + cos (x + \frac{2 π}{3}) - 2

Somar elementos similares:

2 - 2 = 0

= cos (x + \frac{2 π}{3})

Simplificar

\frac{5}{2} - 2 : \frac{1}{2}

\frac{5}{2} - 2

Converter para fração:

2 = \frac{2 \cdot 2}{2}

= - \frac{2 \cdot 2}{2} + \frac{5}{2}

Já que os denominadores são iguais, combinar as frações:

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

= \frac{- 2 \cdot 2 + 5}{2}

- 2 \cdot 2 + 5 = 1

- 2 \cdot 2 + 5

Multiplicar os números:

2 \cdot 2 = 4

= - 4 + 5

Somar/subtrair:

- 4 + 5 = 1

= 1

= \frac{1}{2}

cos (x + \frac{2 π}{3}) = \frac{1}{2}

cos (x + \frac{2 π}{3}) = \frac{1}{2}

cos (x + \frac{2 π}{3}) = \frac{1}{2}

Soluções gerais para

cos (x + \frac{2 π}{3}) = \frac{1}{2}

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}

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

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

Resolver

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

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

Mova

\frac{2 π}{3}

para o lado direito

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

Subtrair

\frac{2 π}{3}

de ambos os lados

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

Simplificar

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

Simplificar

x + \frac{2 π}{3} - \frac{2 π}{3} : x

x + \frac{2 π}{3} - \frac{2 π}{3}

Somar elementos similares:

\frac{2 π}{3} - \frac{2 π}{3} = 0

= x

Simplificar

\frac{π}{3} + 2 πn - \frac{2 π}{3} : 2 πn - \frac{π}{3}

\frac{π}{3} + 2 πn - \frac{2 π}{3}

Agrupar termos semelhantes

= 2 πn + \frac{π}{3} - \frac{2 π}{3}

Combinar as frações usando o mínimo múltiplo comum:

- \frac{π}{3}

Aplicar a regra

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

= \frac{π - 2 π}{3}

Somar elementos similares:

π - 2 π = - π

= \frac{- π}{3}

Aplicar as propriedades das frações:

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

= - \frac{π}{3}

= 2 πn - \frac{π}{3}

x = 2 πn - \frac{π}{3}

x = 2 πn - \frac{π}{3}

x = 2 πn - \frac{π}{3}

Resolver

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

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

Mova

\frac{2 π}{3}

para o lado direito

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

Subtrair

\frac{2 π}{3}

de ambos os lados

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

Simplificar

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

Simplificar

x + \frac{2 π}{3} - \frac{2 π}{3} : x

x + \frac{2 π}{3} - \frac{2 π}{3}

Somar elementos similares:

\frac{2 π}{3} - \frac{2 π}{3} = 0

= x

Simplificar

\frac{5 π}{3} + 2 πn - \frac{2 π}{3} : 2 πn + π

\frac{5 π}{3} + 2 πn - \frac{2 π}{3}

Agrupar termos semelhantes

= 2 πn + \frac{5 π}{3} - \frac{2 π}{3}

Combinar as frações usando o mínimo múltiplo comum:

π

Aplicar a regra

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

= \frac{5 π - 2 π}{3}

Somar elementos similares:

5 π - 2 π = 3 π

= \frac{3 π}{3}

Dividir:

\frac{3}{3} = 1

= π

= 2 πn + π

x = 2 πn + π

x = 2 πn + π

x = 2 πn + π

x = 2 πn - \frac{π}{3}, x = 2 πn + π

Gráfico

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