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Popular Trigonometria >

sin(x/7)=(3^{1/2})/2 ,pi<x<3pi

Solução

sin (\frac{x}{7}) = \frac{3 ^{\frac{1}{2}}}{2}, π < x < 3 π

Solução

x = \frac{7 π}{3}

Graus

x = 42 0^{\circ}

Passos da solução

sin (\frac{x}{7}) = \frac{3 ^{\frac{1}{2}}}{2}, π < x < 3 π

Aplique as propriedades trigonométricas inversas

sin (\frac{x}{7}) = \frac{3 ^{\frac{1}{2}}}{2}

Soluções gerais para

sin (\frac{x}{7}) = \frac{3 ^{\frac{1}{2}}}{2}

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

\frac{x}{7} = arcsin (\frac{3 ^{\frac{1}{2}}}{2}) + 2 πn, \frac{x}{7} = π - arcsin (\frac{3 ^{\frac{1}{2}}}{2}) + 2 πn

\frac{x}{7} = arcsin (\frac{3 ^{\frac{1}{2}}}{2}) + 2 πn, \frac{x}{7} = π - arcsin (\frac{3 ^{\frac{1}{2}}}{2}) + 2 πn

Resolver

\frac{x}{7} = arcsin (\frac{3 ^{\frac{1}{2}}}{2}) + 2 πn : x = \frac{7 π}{3} + 14 πn

\frac{x}{7} = arcsin (\frac{3 ^{\frac{1}{2}}}{2}) + 2 πn

Simplificar

arcsin (\frac{3 ^{\frac{1}{2}}}{2}) + 2 πn : \frac{π}{3} + 2 πn

arcsin (\frac{3 ^{\frac{1}{2}}}{2}) + 2 πn

Utilizar a seguinte identidade trivial:

arcsin (\frac{3 ^{\frac{1}{2}}}{2}) = \frac{π}{3}

x 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 arcsin (x) 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} arcsin (x) 0^{\circ} 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ}

= \frac{π}{3} + 2 πn

\frac{x}{7} = \frac{π}{3} + 2 πn

Multiplicar ambos os lados por

7

\frac{x}{7} = \frac{π}{3} + 2 πn

Multiplicar ambos os lados por

7

\frac{7 x}{7} = 7 \cdot \frac{π}{3} + 7 \cdot 2 πn

Simplificar

\frac{7 x}{7} = 7 \cdot \frac{π}{3} + 7 \cdot 2 πn

Simplificar

\frac{7 x}{7} : x

\frac{7 x}{7}

Dividir:

\frac{7}{7} = 1

= x

Simplificar

7 \cdot \frac{π}{3} + 7 \cdot 2 πn : \frac{7 π}{3} + 14 πn

7 \cdot \frac{π}{3} + 7 \cdot 2 πn

Multiplicar

7 \cdot \frac{π}{3} : \frac{7 π}{3}

7 \cdot \frac{π}{3}

Multiplicar frações:

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

= \frac{π 7}{3}

= \frac{7 π}{3} + 7 \cdot 2 πn

Multiplicar os números:

7 \cdot 2 = 14

= \frac{7 π}{3} + 14 πn

x = \frac{7 π}{3} + 14 πn

x = \frac{7 π}{3} + 14 πn

x = \frac{7 π}{3} + 14 πn

Resolver

\frac{x}{7} = π - arcsin (\frac{3 ^{\frac{1}{2}}}{2}) + 2 πn : x = 7 π - \frac{7 π}{3} + 14 πn

\frac{x}{7} = π - arcsin (\frac{3 ^{\frac{1}{2}}}{2}) + 2 πn

Simplificar

π - arcsin (\frac{3 ^{\frac{1}{2}}}{2}) + 2 πn : π - \frac{π}{3} + 2 πn

π - arcsin (\frac{3 ^{\frac{1}{2}}}{2}) + 2 πn

Utilizar a seguinte identidade trivial:

arcsin (\frac{3 ^{\frac{1}{2}}}{2}) = \frac{π}{3}

x 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 arcsin (x) 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} arcsin (x) 0^{\circ} 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ}

= π - \frac{π}{3} + 2 πn

\frac{x}{7} = π - \frac{π}{3} + 2 πn

Multiplicar ambos os lados por

7

\frac{x}{7} = π - \frac{π}{3} + 2 πn

Multiplicar ambos os lados por

7

\frac{7 x}{7} = 7 π - 7 \cdot \frac{π}{3} + 7 \cdot 2 πn

Simplificar

\frac{7 x}{7} = 7 π - 7 \cdot \frac{π}{3} + 7 \cdot 2 πn

Simplificar

\frac{7 x}{7} : x

\frac{7 x}{7}

Dividir:

\frac{7}{7} = 1

= x

Simplificar

7 π - 7 \cdot \frac{π}{3} + 7 \cdot 2 πn : 7 π - \frac{7 π}{3} + 14 πn

7 π - 7 \cdot \frac{π}{3} + 7 \cdot 2 πn

Multiplicar

7 \cdot \frac{π}{3} : \frac{7 π}{3}

7 \cdot \frac{π}{3}

Multiplicar frações:

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

= \frac{π 7}{3}

= 7 π - \frac{7 π}{3} + 7 \cdot 2 πn

Multiplicar os números:

7 \cdot 2 = 14

= 7 π - \frac{7 π}{3} + 14 πn

x = 7 π - \frac{7 π}{3} + 14 πn

x = 7 π - \frac{7 π}{3} + 14 πn

x = 7 π - \frac{7 π}{3} + 14 πn

x = \frac{7 π}{3} + 14 πn, x = 7 π - \frac{7 π}{3} + 14 πn

Soluções para o intervalo

π < x < 3 π

x = \frac{7 π}{3}

Gráfico

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