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Popular Trigonometria >

sqrt(11)sin(x+37.09)=1

Solução

11 sin (x + 37.0 9^{\circ}) = 1

Solução

x = 0.30627 \dots + 36 0^{\circ} n - 37.08999 \dots^{\circ}, x = 18 0^{\circ} - 0.30627 \dots + 36 0^{\circ} n - 37.08999 \dots^{\circ}

Radianos

x = 0.30627 \dots - \frac{245 π}{1189} + 2 πn, x = π - 0.30627 \dots - \frac{245 π}{1189} + 2 πn

Passos da solução

11 sin (x + 37.0 9^{\circ}) = 1

Dividir ambos os lados por

11

11 sin (x + 37.08999 \dots^{\circ}) = 1

Dividir ambos os lados por

11

\frac{11 sin ( x + 37.08999 \dots ^{\circ} )}{11} = \frac{1}{11}

Simplificar

\frac{11 sin ( x + 37.08999 \dots ^{\circ} )}{11} = \frac{1}{11}

Simplificar

\frac{11 sin ( x + 37.08999 \dots ^{\circ} )}{11} : sin (x + 37.08999 \dots^{\circ})

\frac{11 sin ( x + 37.08999 \dots ^{\circ} )}{11}

Eliminar o fator comum:

11

= sin (x + 37.08999 \dots^{\circ})

Simplificar

\frac{1}{11} : \frac{11}{11}

\frac{1}{11}

Multiplicar pelo conjugado

\frac{11}{11}

= \frac{1 \cdot 11}{11 11}

1 \cdot 11 = 11

1111 = 11

1111

Aplicar as propriedades dos radicais:

a a = a

1111 = 11

= 11

= \frac{11}{11}

sin (x + 37.08999 \dots^{\circ}) = \frac{11}{11}

sin (x + 37.08999 \dots^{\circ}) = \frac{11}{11}

sin (x + 37.08999 \dots^{\circ}) = \frac{11}{11}

Aplique as propriedades trigonométricas inversas

sin (x + 37.08999 \dots^{\circ}) = \frac{11}{11}

Soluções gerais para

sin (x + 37.08999 \dots^{\circ}) = \frac{11}{11}

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

x + 37.08999 \dots^{\circ} = arcsin (\frac{11}{11}) + 36 0^{\circ} n, x + 37.08999 \dots^{\circ} = 18 0^{\circ} - arcsin (\frac{11}{11}) + 36 0^{\circ} n

x + 37.08999 \dots^{\circ} = arcsin (\frac{11}{11}) + 36 0^{\circ} n, x + 37.08999 \dots^{\circ} = 18 0^{\circ} - arcsin (\frac{11}{11}) + 36 0^{\circ} n

Resolver

x + 37.08999 \dots^{\circ} = arcsin (\frac{11}{11}) + 36 0^{\circ} n : x = arcsin (\frac{1}{11}) + 36 0^{\circ} n - 37.08999 \dots^{\circ}

x + 37.08999 \dots^{\circ} = arcsin (\frac{11}{11}) + 36 0^{\circ} n

Simplificar

arcsin (\frac{11}{11}) + 36 0^{\circ} n : arcsin (\frac{1}{11}) + 36 0^{\circ} n

arcsin (\frac{11}{11}) + 36 0^{\circ} n

\frac{11}{11} = \frac{1}{11}

\frac{11}{11}

Aplicar as propriedades dos radicais:

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

11 = 1 1^{\frac{1}{2}}

= \frac{1 1 ^{\frac{1}{2}}}{11}

Aplicar as propriedades dos expoentes:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

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

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

Subtrair:

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

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

Aplicar as propriedades dos radicais:

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

1 1^{\frac{1}{2}} = 11

= \frac{1}{11}

= arcsin (\frac{1}{11}) + 36 0^{\circ} n

x + 37.08999 \dots^{\circ} = arcsin (\frac{1}{11}) + 36 0^{\circ} n

Mova

37.08999 \dots^{\circ}

para o lado direito

x + 37.08999 \dots^{\circ} = arcsin (\frac{1}{11}) + 36 0^{\circ} n

Subtrair

37.08999 \dots^{\circ}

de ambos os lados

x + 37.08999 \dots^{\circ} - 37.08999 \dots^{\circ} = arcsin (\frac{1}{11}) + 36 0^{\circ} n - 37.08999 \dots^{\circ}

Simplificar

x = arcsin (\frac{1}{11}) + 36 0^{\circ} n - 37.08999 \dots^{\circ}

x = arcsin (\frac{1}{11}) + 36 0^{\circ} n - 37.08999 \dots^{\circ}

Resolver

x + 37.08999 \dots^{\circ} = 18 0^{\circ} - arcsin (\frac{11}{11}) + 36 0^{\circ} n : x = 18 0^{\circ} - arcsin (\frac{1}{11}) + 36 0^{\circ} n - 37.08999 \dots^{\circ}

x + 37.08999 \dots^{\circ} = 18 0^{\circ} - arcsin (\frac{11}{11}) + 36 0^{\circ} n

Simplificar

18 0^{\circ} - arcsin (\frac{11}{11}) + 36 0^{\circ} n : 18 0^{\circ} - arcsin (\frac{1}{11}) + 36 0^{\circ} n

18 0^{\circ} - arcsin (\frac{11}{11}) + 36 0^{\circ} n

\frac{11}{11} = \frac{1}{11}

\frac{11}{11}

Aplicar as propriedades dos radicais:

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

11 = 1 1^{\frac{1}{2}}

= \frac{1 1 ^{\frac{1}{2}}}{11}

Aplicar as propriedades dos expoentes:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

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

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

Subtrair:

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

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

Aplicar as propriedades dos radicais:

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

1 1^{\frac{1}{2}} = 11

= \frac{1}{11}

= 18 0^{\circ} - arcsin (\frac{1}{11}) + 36 0^{\circ} n

x + 37.08999 \dots^{\circ} = 18 0^{\circ} - arcsin (\frac{1}{11}) + 36 0^{\circ} n

Mova

37.08999 \dots^{\circ}

para o lado direito

x + 37.08999 \dots^{\circ} = 18 0^{\circ} - arcsin (\frac{1}{11}) + 36 0^{\circ} n

Subtrair

37.08999 \dots^{\circ}

de ambos os lados

x + 37.08999 \dots^{\circ} - 37.08999 \dots^{\circ} = 18 0^{\circ} - arcsin (\frac{1}{11}) + 36 0^{\circ} n - 37.08999 \dots^{\circ}

Simplificar

x = 18 0^{\circ} - arcsin (\frac{1}{11}) + 36 0^{\circ} n - 37.08999 \dots^{\circ}

x = 18 0^{\circ} - arcsin (\frac{1}{11}) + 36 0^{\circ} n - 37.08999 \dots^{\circ}

x = arcsin (\frac{1}{11}) + 36 0^{\circ} n - 37.08999 \dots^{\circ}, x = 18 0^{\circ} - arcsin (\frac{1}{11}) + 36 0^{\circ} n - 37.08999 \dots^{\circ}

Mostrar soluções na forma decimal

x = 0.30627 \dots + 36 0^{\circ} n - 37.08999 \dots^{\circ}, x = 18 0^{\circ} - 0.30627 \dots + 36 0^{\circ} n - 37.08999 \dots^{\circ}

Gráfico

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