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Popular Trigonometria >

2/3 =(sin(x))/(sin(135))

Solução

\frac{2}{3} = \frac{sin ( x )}{sin ( 13 5 ^{\circ} )}

Solução

x = 0.49088 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.49088 \dots + 36 0^{\circ} n

+1

Radianos

x = 0.49088 \dots + 2 πn, x = π - 0.49088 \dots + 2 πn

Passos da solução

\frac{2}{3} = \frac{sin ( x )}{sin ( 13 5 ^{\circ} )}

Trocar lados

\frac{sin ( x )}{sin ( 13 5 ^{\circ} )} = \frac{2}{3}

sin (13 5^{\circ}) = \frac{2}{2}

sin (13 5^{\circ})

Utilizar a seguinte identidade trivial:

sin (13 5^{\circ}) = \frac{2}{2}

sin (13 5^{\circ})

sin (x)

tabela de periodicidade com ciclo de

36 0^{\circ} n

:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{2}{2}

= \frac{2}{2}

\frac{sin ( x )}{\frac{2}{2}} = \frac{2}{3}

Multiplicar ambos os lados por

\frac{2}{2}

\frac{sin ( x )}{\frac{2}{2}} = \frac{2}{3}

Multiplicar ambos os lados por

\frac{2}{2}

\frac{sin ( x ) \frac{2}{2}}{\frac{2}{2}} = \frac{2 \cdot \frac{2}{2}}{3}

Simplificar

\frac{sin ( x ) \frac{2}{2}}{\frac{2}{2}} = \frac{2 \cdot \frac{2}{2}}{3}

Simplificar

\frac{sin ( x ) \frac{2}{2}}{\frac{2}{2}} : sin (x)

\frac{sin ( x ) \frac{2}{2}}{\frac{2}{2}}

Aplicar as propriedades das frações:

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

= \frac{sin ( x ) \frac{2}{2} \cdot 2}{2}

Multiplicar

sin (x) \frac{2}{2} \cdot 2 : 2 sin (x)

sin (x) \frac{2}{2} \cdot 2

Multiplicar frações:

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

= \frac{2 sin ( x ) \cdot 2}{2}

Eliminar o fator comum:

2

= 2 sin (x)

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

Eliminar o fator comum:

2

= sin (x)

Simplificar

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

\frac{2 \cdot \frac{2}{2}}{3}

Multiplicar

2 \cdot \frac{2}{2} : 2

2 \cdot \frac{2}{2}

Multiplicar frações:

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

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

Eliminar o fator comum:

2

= 2

= \frac{2}{3}

sin (x) = \frac{2}{3}

sin (x) = \frac{2}{3}

sin (x) = \frac{2}{3}

Aplique as propriedades trigonométricas inversas

sin (x) = \frac{2}{3}

Soluções gerais para

sin (x) = \frac{2}{3}

sin (x) = a \Rightarrow x = arcsin (a) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (a) + 36 0^{\circ} n

x = arcsin (\frac{2}{3}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{2}{3}) + 36 0^{\circ} n

x = arcsin (\frac{2}{3}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{2}{3}) + 36 0^{\circ} n

Mostrar soluções na forma decimal

x = 0.49088 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.49088 \dots + 36 0^{\circ} n

Gráfico

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