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Popular Trigonometria >

1/2-cos(x/2)=0

Solução

\frac{1}{2} - cos (\frac{x}{2}) = 0

Solução

x = \frac{2 π}{3} + 4 πn, x = \frac{10 π}{3} + 4 πn

Graus

x = 12 0^{\circ} + 72 0^{\circ} n, x = 60 0^{\circ} + 72 0^{\circ} n

Passos da solução

\frac{1}{2} - cos (\frac{x}{2}) = 0

Mova

\frac{1}{2}

para o lado direito

\frac{1}{2} - cos (\frac{x}{2}) = 0

Subtrair

\frac{1}{2}

de ambos os lados

\frac{1}{2} - cos (\frac{x}{2}) - \frac{1}{2} = 0 - \frac{1}{2}

Simplificar

- cos (\frac{x}{2}) = - \frac{1}{2}

- cos (\frac{x}{2}) = - \frac{1}{2}

Dividir ambos os lados por

- 1

- cos (\frac{x}{2}) = - \frac{1}{2}

Dividir ambos os lados por

- 1

\frac{- cos ( \frac{x}{2} )}{- 1} = \frac{- \frac{1}{2}}{- 1}

Simplificar

\frac{- cos ( \frac{x}{2} )}{- 1} = \frac{- \frac{1}{2}}{- 1}

Simplificar

\frac{- cos ( \frac{x}{2} )}{- 1} : cos (\frac{x}{2})

\frac{- cos ( \frac{x}{2} )}{- 1}

Aplicar as propriedades das frações:

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

= \frac{cos ( \frac{x}{2} )}{1}

Aplicar a regra

\frac{a}{1} = a

= cos (\frac{x}{2})

Simplificar

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

\frac{- \frac{1}{2}}{- 1}

Aplicar as propriedades das frações:

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

= \frac{\frac{1}{2}}{1}

Aplicar as propriedades das frações:

\frac{a}{1} = a

= \frac{1}{2}

cos (\frac{x}{2}) = \frac{1}{2}

cos (\frac{x}{2}) = \frac{1}{2}

cos (\frac{x}{2}) = \frac{1}{2}

Soluções gerais para

cos (\frac{x}{2}) = \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}

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

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

Resolver

\frac{x}{2} = \frac{π}{3} + 2 πn : x = \frac{2 π}{3} + 4 πn

\frac{x}{2} = \frac{π}{3} + 2 πn

Multiplicar ambos os lados por

2

\frac{x}{2} = \frac{π}{3} + 2 πn

Multiplicar ambos os lados por

2

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

Simplificar

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

Simplificar

\frac{2 x}{2} : x

\frac{2 x}{2}

Dividir:

\frac{2}{2} = 1

= x

Simplificar

2 \cdot \frac{π}{3} + 2 \cdot 2 πn : \frac{2 π}{3} + 4 πn

2 \cdot \frac{π}{3} + 2 \cdot 2 πn

Multiplicar

2 \cdot \frac{π}{3} : \frac{2 π}{3}

2 \cdot \frac{π}{3}

Multiplicar frações:

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

= \frac{π 2}{3}

= \frac{2 π}{3} + 2 \cdot 2 πn

Multiplicar os números:

2 \cdot 2 = 4

= \frac{2 π}{3} + 4 πn

x = \frac{2 π}{3} + 4 πn

x = \frac{2 π}{3} + 4 πn

x = \frac{2 π}{3} + 4 πn

Resolver

\frac{x}{2} = \frac{5 π}{3} + 2 πn : x = \frac{10 π}{3} + 4 πn

\frac{x}{2} = \frac{5 π}{3} + 2 πn

Multiplicar ambos os lados por

2

\frac{x}{2} = \frac{5 π}{3} + 2 πn

Multiplicar ambos os lados por

2

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

Simplificar

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

Simplificar

\frac{2 x}{2} : x

\frac{2 x}{2}

Dividir:

\frac{2}{2} = 1

= x

Simplificar

2 \cdot \frac{5 π}{3} + 2 \cdot 2 πn : \frac{10 π}{3} + 4 πn

2 \cdot \frac{5 π}{3} + 2 \cdot 2 πn

2 \cdot \frac{5 π}{3} = \frac{10 π}{3}

2 \cdot \frac{5 π}{3}

Multiplicar frações:

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

= \frac{5 π 2}{3}

Multiplicar os números:

5 \cdot 2 = 10

= \frac{10 π}{3}

2 \cdot 2 πn = 4 πn

2 \cdot 2 πn

Multiplicar os números:

2 \cdot 2 = 4

= 4 πn

= \frac{10 π}{3} + 4 πn

x = \frac{10 π}{3} + 4 πn

x = \frac{10 π}{3} + 4 πn

x = \frac{10 π}{3} + 4 πn

x = \frac{2 π}{3} + 4 πn, x = \frac{10 π}{3} + 4 πn

Gráfico

Exemplos populares

csc(θ)=(sqrt(28))/2 ,sin(θ)