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Popular Trigonometria >

sin(x/2+pi)= 3/(2sqrt(3))

Solução

sin (\frac{x}{2} + π) = \frac{3}{2 3}

Solução

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

Radianos

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

Passos da solução

sin (\frac{x}{2} + π) = \frac{3}{2 3}

Simplificar

\frac{3}{2 3} : \frac{3}{2}

\frac{3}{2 3}

Aplicar as propriedades dos radicais:

n a = a^{\frac{1}{n}}

3 = 3^{\frac{1}{2}}

= \frac{3}{2 \cdot 3 ^{\frac{1}{2}}}

Aplicar as propriedades dos expoentes:

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

\frac{3 ^{1}}{3 ^{\frac{1}{2}}} = 3^{1 - \frac{1}{2}}

= \frac{3 ^{1 - \frac{1}{2}}}{2}

Subtrair:

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

= \frac{3 ^{\frac{1}{2}}}{2}

Aplicar as propriedades dos radicais:

a^{\frac{1}{n}} = n a

3^{\frac{1}{2}} = 3

= \frac{3}{2}

Soluções gerais para

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

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

Resolver

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

\frac{x}{2} + π = \frac{π}{3} + 2 πn

Mova

π

para o lado direito

\frac{x}{2} + π = \frac{π}{3} + 2 πn

Subtrair

π

de ambos os lados

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

Simplificar

\frac{x}{2} = \frac{π}{3} + 2 πn - π

\frac{x}{2} = \frac{π}{3} + 2 πn - π

Multiplicar ambos os lados por

2

\frac{x}{2} = \frac{π}{3} + 2 πn - π

Multiplicar ambos os lados por

2

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

Simplificar

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

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 - 2 π : \frac{2 π}{3} + 4 πn - 2 π

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

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 - 2 π

Multiplicar os números:

2 \cdot 2 = 4

= \frac{2 π}{3} + 4 πn - 2 π

x = \frac{2 π}{3} + 4 πn - 2 π

x = \frac{2 π}{3} + 4 πn - 2 π

x = \frac{2 π}{3} + 4 πn - 2 π

Resolver

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

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

Mova

π

para o lado direito

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

Subtrair

π

de ambos os lados

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

Simplificar

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

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

Multiplicar ambos os lados por

2

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

Multiplicar ambos os lados por

2

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

Simplificar

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

Simplificar

\frac{2 x}{2} : x

\frac{2 x}{2}

Dividir:

\frac{2}{2} = 1

= x

Simplificar

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

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

2 \cdot \frac{2 π}{3} = \frac{4 π}{3}

2 \cdot \frac{2 π}{3}

Multiplicar frações:

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

= \frac{2 π 2}{3}

Multiplicar os números:

2 \cdot 2 = 4

= \frac{4 π}{3}

2 \cdot 2 πn = 4 πn

2 \cdot 2 πn

Multiplicar os números:

2 \cdot 2 = 4

= 4 πn

= \frac{4 π}{3} + 4 πn - 2 π

x = \frac{4 π}{3} + 4 πn - 2 π

x = \frac{4 π}{3} + 4 πn - 2 π

x = \frac{4 π}{3} + 4 πn - 2 π

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

Gráfico

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