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Popular Trigonometria >

6sin(2x-30)+2=0

Solução

6 sin (2 x - 3 0^{\circ}) + 2 = 0

Solução

x = 18 0^{\circ} n + 1 5^{\circ} - \frac{0.33983 \dots}{2}, x = 18 0^{\circ} n + 9 0^{\circ} + 1 5^{\circ} + \frac{0.33983 \dots}{2}

Radianos

x = \frac{π}{12} - \frac{0.33983 \dots}{2} + πn, x = \frac{π}{2} + \frac{π}{12} + \frac{0.33983 \dots}{2} + πn

Passos da solução

6 sin (2 x - 3 0^{\circ}) + 2 = 0

Mova

2

para o lado direito

6 sin (2 x - 3 0^{\circ}) + 2 = 0

Subtrair

2

de ambos os lados

6 sin (2 x - 3 0^{\circ}) + 2 - 2 = 0 - 2

Simplificar

6 sin (2 x - 3 0^{\circ}) = - 2

6 sin (2 x - 3 0^{\circ}) = - 2

Dividir ambos os lados por

6

6 sin (2 x - 3 0^{\circ}) = - 2

Dividir ambos os lados por

6

\frac{6 sin ( 2 x - 3 0 ^{\circ} )}{6} = \frac{- 2}{6}

Simplificar

\frac{6 sin ( 2 x - 3 0 ^{\circ} )}{6} = \frac{- 2}{6}

Simplificar

\frac{6 sin ( 2 x - 3 0 ^{\circ} )}{6} : sin (2 x - 3 0^{\circ})

\frac{6 sin ( 2 x - 3 0 ^{\circ} )}{6}

Dividir:

\frac{6}{6} = 1

= sin (2 x - 3 0^{\circ})

Simplificar

\frac{- 2}{6} : - \frac{1}{3}

\frac{- 2}{6}

Aplicar as propriedades das frações:

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

= - \frac{2}{6}

Eliminar o fator comum:

2

= - \frac{1}{3}

sin (2 x - 3 0^{\circ}) = - \frac{1}{3}

sin (2 x - 3 0^{\circ}) = - \frac{1}{3}

sin (2 x - 3 0^{\circ}) = - \frac{1}{3}

Aplique as propriedades trigonométricas inversas

sin (2 x - 3 0^{\circ}) = - \frac{1}{3}

Soluções gerais para

sin (2 x - 3 0^{\circ}) = - \frac{1}{3}

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

2 x - 3 0^{\circ} = arcsin (- \frac{1}{3}) + 36 0^{\circ} n, 2 x - 3 0^{\circ} = 18 0^{\circ} + arcsin (\frac{1}{3}) + 36 0^{\circ} n

2 x - 3 0^{\circ} = arcsin (- \frac{1}{3}) + 36 0^{\circ} n, 2 x - 3 0^{\circ} = 18 0^{\circ} + arcsin (\frac{1}{3}) + 36 0^{\circ} n

Resolver

2 x - 3 0^{\circ} = arcsin (- \frac{1}{3}) + 36 0^{\circ} n : x = 18 0^{\circ} n + 1 5^{\circ} - \frac{arcsin ( \frac{1}{3} )}{2}

2 x - 3 0^{\circ} = arcsin (- \frac{1}{3}) + 36 0^{\circ} n

Simplificar

arcsin (- \frac{1}{3}) + 36 0^{\circ} n : - arcsin (\frac{1}{3}) + 36 0^{\circ} n

arcsin (- \frac{1}{3}) + 36 0^{\circ} n

Utilizar a seguinte propriedade:

arcsin (- x) = - arcsin (x)

arcsin (- \frac{1}{3}) = - arcsin (\frac{1}{3})

= - arcsin (\frac{1}{3}) + 36 0^{\circ} n

2 x - 3 0^{\circ} = - arcsin (\frac{1}{3}) + 36 0^{\circ} n

Mova

3 0^{\circ}

para o lado direito

2 x - 3 0^{\circ} = - arcsin (\frac{1}{3}) + 36 0^{\circ} n

Adicionar

3 0^{\circ}

a ambos os lados

2 x - 3 0^{\circ} + 3 0^{\circ} = - arcsin (\frac{1}{3}) + 36 0^{\circ} n + 3 0^{\circ}

Simplificar

2 x = - arcsin (\frac{1}{3}) + 36 0^{\circ} n + 3 0^{\circ}

2 x = - arcsin (\frac{1}{3}) + 36 0^{\circ} n + 3 0^{\circ}

Dividir ambos os lados por

2

2 x = - arcsin (\frac{1}{3}) + 36 0^{\circ} n + 3 0^{\circ}

Dividir ambos os lados por

2

\frac{2 x}{2} = - \frac{arcsin ( \frac{1}{3} )}{2} + \frac{36 0 ^{\circ} n}{2} + \frac{3 0 ^{\circ}}{2}

Simplificar

\frac{2 x}{2} = - \frac{arcsin ( \frac{1}{3} )}{2} + \frac{36 0 ^{\circ} n}{2} + \frac{3 0 ^{\circ}}{2}

Simplificar

\frac{2 x}{2} : x

\frac{2 x}{2}

Dividir:

\frac{2}{2} = 1

= x

Simplificar

- \frac{arcsin ( \frac{1}{3} )}{2} + \frac{36 0 ^{\circ} n}{2} + \frac{3 0 ^{\circ}}{2} : 18 0^{\circ} n + 1 5^{\circ} - \frac{arcsin ( \frac{1}{3} )}{2}

- \frac{arcsin ( \frac{1}{3} )}{2} + \frac{36 0 ^{\circ} n}{2} + \frac{3 0 ^{\circ}}{2}

Agrupar termos semelhantes

= \frac{36 0 ^{\circ} n}{2} + \frac{3 0 ^{\circ}}{2} - \frac{arcsin ( \frac{1}{3} )}{2}

\frac{36 0 ^{\circ} n}{2} = 18 0^{\circ} n

\frac{36 0 ^{\circ} n}{2}

Dividir:

\frac{2}{2} = 1

= 18 0^{\circ} n

\frac{3 0 ^{\circ}}{2} = 1 5^{\circ}

\frac{3 0 ^{\circ}}{2}

Aplicar as propriedades das frações:

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

= \frac{18 0 ^{\circ}}{6 \cdot 2}

Multiplicar os números:

6 \cdot 2 = 12

= 1 5^{\circ}

= 18 0^{\circ} n + 1 5^{\circ} - \frac{arcsin ( \frac{1}{3} )}{2}

x = 18 0^{\circ} n + 1 5^{\circ} - \frac{arcsin ( \frac{1}{3} )}{2}

x = 18 0^{\circ} n + 1 5^{\circ} - \frac{arcsin ( \frac{1}{3} )}{2}

x = 18 0^{\circ} n + 1 5^{\circ} - \frac{arcsin ( \frac{1}{3} )}{2}

Resolver

2 x - 3 0^{\circ} = 18 0^{\circ} + arcsin (\frac{1}{3}) + 36 0^{\circ} n : x = 18 0^{\circ} n + 9 0^{\circ} + 1 5^{\circ} + \frac{arcsin ( \frac{1}{3} )}{2}

2 x - 3 0^{\circ} = 18 0^{\circ} + arcsin (\frac{1}{3}) + 36 0^{\circ} n

Mova

3 0^{\circ}

para o lado direito

2 x - 3 0^{\circ} = 18 0^{\circ} + arcsin (\frac{1}{3}) + 36 0^{\circ} n

Adicionar

3 0^{\circ}

a ambos os lados

2 x - 3 0^{\circ} + 3 0^{\circ} = 18 0^{\circ} + arcsin (\frac{1}{3}) + 36 0^{\circ} n + 3 0^{\circ}

Simplificar

2 x = 18 0^{\circ} + arcsin (\frac{1}{3}) + 36 0^{\circ} n + 3 0^{\circ}

2 x = 18 0^{\circ} + arcsin (\frac{1}{3}) + 36 0^{\circ} n + 3 0^{\circ}

Dividir ambos os lados por

2

2 x = 18 0^{\circ} + arcsin (\frac{1}{3}) + 36 0^{\circ} n + 3 0^{\circ}

Dividir ambos os lados por

2

\frac{2 x}{2} = 9 0^{\circ} + \frac{arcsin ( \frac{1}{3} )}{2} + \frac{36 0 ^{\circ} n}{2} + \frac{3 0 ^{\circ}}{2}

Simplificar

\frac{2 x}{2} = 9 0^{\circ} + \frac{arcsin ( \frac{1}{3} )}{2} + \frac{36 0 ^{\circ} n}{2} + \frac{3 0 ^{\circ}}{2}

Simplificar

\frac{2 x}{2} : x

\frac{2 x}{2}

Dividir:

\frac{2}{2} = 1

= x

Simplificar

9 0^{\circ} + \frac{arcsin ( \frac{1}{3} )}{2} + \frac{36 0 ^{\circ} n}{2} + \frac{3 0 ^{\circ}}{2} : 18 0^{\circ} n + 9 0^{\circ} + 1 5^{\circ} + \frac{arcsin ( \frac{1}{3} )}{2}

9 0^{\circ} + \frac{arcsin ( \frac{1}{3} )}{2} + \frac{36 0 ^{\circ} n}{2} + \frac{3 0 ^{\circ}}{2}

Agrupar termos semelhantes

= 9 0^{\circ} + \frac{36 0 ^{\circ} n}{2} + \frac{3 0 ^{\circ}}{2} + \frac{arcsin ( \frac{1}{3} )}{2}

\frac{36 0 ^{\circ} n}{2} = 18 0^{\circ} n

\frac{36 0 ^{\circ} n}{2}

Dividir:

\frac{2}{2} = 1

= 18 0^{\circ} n

\frac{3 0 ^{\circ}}{2} = 1 5^{\circ}

\frac{3 0 ^{\circ}}{2}

Aplicar as propriedades das frações:

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

= \frac{18 0 ^{\circ}}{6 \cdot 2}

Multiplicar os números:

6 \cdot 2 = 12

= 1 5^{\circ}

= 9 0^{\circ} + 18 0^{\circ} n + 1 5^{\circ} + \frac{arcsin ( \frac{1}{3} )}{2}

Agrupar termos semelhantes

= 18 0^{\circ} n + 9 0^{\circ} + 1 5^{\circ} + \frac{arcsin ( \frac{1}{3} )}{2}

x = 18 0^{\circ} n + 9 0^{\circ} + 1 5^{\circ} + \frac{arcsin ( \frac{1}{3} )}{2}

x = 18 0^{\circ} n + 9 0^{\circ} + 1 5^{\circ} + \frac{arcsin ( \frac{1}{3} )}{2}

x = 18 0^{\circ} n + 9 0^{\circ} + 1 5^{\circ} + \frac{arcsin ( \frac{1}{3} )}{2}

x = 18 0^{\circ} n + 1 5^{\circ} - \frac{arcsin ( \frac{1}{3} )}{2}, x = 18 0^{\circ} n + 9 0^{\circ} + 1 5^{\circ} + \frac{arcsin ( \frac{1}{3} )}{2}

Mostrar soluções na forma decimal

x = 18 0^{\circ} n + 1 5^{\circ} - \frac{0.33983 \dots}{2}, x = 18 0^{\circ} n + 9 0^{\circ} + 1 5^{\circ} + \frac{0.33983 \dots}{2}

Gráfico

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