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solvefor n,sin(x)+sin(13 n/2-x)=1

Solução

resolver para

n, sin (x) + sin (13 \frac{n}{2} - x) = 1

Solução

n = \frac{2 arcsin ( 1 - sin ( x ) )}{13} + \frac{4 πk}{13} + \frac{2 x}{13}, n = \frac{2 π}{13} + \frac{2 arcsin ( - 1 + sin ( x ) )}{13} + \frac{4 πk}{13} + \frac{2 x}{13}

Passos da solução

sin (x) + sin (13 \cdot \frac{n}{2} - x) = 1

Mova

sin (x)

para o lado direito

sin (x) + sin (13 \frac{n}{2} - x) = 1

Subtrair

sin (x)

de ambos os lados

sin (x) + sin (13 \frac{n}{2} - x) - sin (x) = 1 - sin (x)

Simplificar

sin (13 \frac{n}{2} - x) = 1 - sin (x)

sin (13 \frac{n}{2} - x) = 1 - sin (x)

Aplique as propriedades trigonométricas inversas

sin (13 \cdot \frac{n}{2} - x) = 1 - sin (x)

Soluções gerais para

sin (13 \frac{n}{2} - x) = 1 - sin (x)

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

13 \cdot \frac{n}{2} - x = arcsin (1 - sin (x)) + 2 πk, 13 \cdot \frac{n}{2} - x = π + arcsin (- 1 + sin (x)) + 2 πk

13 \cdot \frac{n}{2} - x = arcsin (1 - sin (x)) + 2 πk, 13 \cdot \frac{n}{2} - x = π + arcsin (- 1 + sin (x)) + 2 πk

Resolver

13 \cdot \frac{n}{2} - x = arcsin (1 - sin (x)) + 2 πk : n = \frac{2 arcsin ( 1 - sin ( x ) )}{13} + \frac{4 πk}{13} + \frac{2 x}{13}

13 \cdot \frac{n}{2} - x = arcsin (1 - sin (x)) + 2 πk

Mova

x

para o lado direito

13 \cdot \frac{n}{2} - x = arcsin (1 - sin (x)) + 2 πk

Adicionar

x

a ambos os lados

13 \cdot \frac{n}{2} - x + x = arcsin (1 - sin (x)) + 2 πk + x

Simplificar

13 \cdot \frac{n}{2} = arcsin (1 - sin (x)) + 2 πk + x

13 \cdot \frac{n}{2} = arcsin (1 - sin (x)) + 2 πk + x

Simplificar

13 \cdot \frac{n}{2} : \frac{13 n}{2}

13 \cdot \frac{n}{2}

Multiplicar frações:

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

= \frac{n \cdot 13}{2}

\frac{13 n}{2} = arcsin (1 - sin (x)) + 2 πk + x

Multiplicar ambos os lados por

2

\frac{13 n}{2} = arcsin (1 - sin (x)) + 2 πk + x

Multiplicar ambos os lados por

2

\frac{13 n}{2} \cdot 2 = arcsin (1 - sin (x)) \cdot 2 + 2 πk \cdot 2 + x \cdot 2

Simplificar

\frac{13 n}{2} \cdot 2 = arcsin (1 - sin (x)) \cdot 2 + 2 πk \cdot 2 + x \cdot 2

Simplificar

\frac{13 n}{2} \cdot 2 : 13 n

\frac{13 n}{2} \cdot 2

Multiplicar frações:

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

= \frac{13 n \cdot 2}{2}

Eliminar o fator comum:

2

= 13 n

Simplificar

arcsin (1 - sin (x)) \cdot 2 : 2 arcsin (1 - sin (x))

arcsin (1 - sin (x)) \cdot 2

Aplique a regra comutativa:

arcsin (1 - sin (x)) \cdot 2 = 2 arcsin (1 - sin (x))

2 arcsin (1 - sin (x))

Simplificar

2 πk \cdot 2 : 4 πk

2 πk \cdot 2

Multiplicar os números:

2 \cdot 2 = 4

= 4 πk

Simplificar

x \cdot 2 : 2 x

x \cdot 2

Aplique a regra comutativa:

x \cdot 2 = 2 x

2 x

13 n = 2 arcsin (1 - sin (x)) + 4 πk + 2 x

13 n = 2 arcsin (1 - sin (x)) + 4 πk + 2 x

13 n = 2 arcsin (1 - sin (x)) + 4 πk + 2 x

Dividir ambos os lados por

13

13 n = 2 arcsin (1 - sin (x)) + 4 πk + 2 x

Dividir ambos os lados por

13

\frac{13 n}{13} = \frac{2 arcsin ( 1 - sin ( x ) )}{13} + \frac{4 πk}{13} + \frac{2 x}{13}

Simplificar

n = \frac{2 arcsin ( 1 - sin ( x ) )}{13} + \frac{4 πk}{13} + \frac{2 x}{13}

n = \frac{2 arcsin ( 1 - sin ( x ) )}{13} + \frac{4 πk}{13} + \frac{2 x}{13}

Resolver

13 \cdot \frac{n}{2} - x = π + arcsin (- 1 + sin (x)) + 2 πk : n = \frac{2 π}{13} + \frac{2 arcsin ( - 1 + sin ( x ) )}{13} + \frac{4 πk}{13} + \frac{2 x}{13}

13 \cdot \frac{n}{2} - x = π + arcsin (- 1 + sin (x)) + 2 πk

Mova

x

para o lado direito

13 \cdot \frac{n}{2} - x = π + arcsin (- 1 + sin (x)) + 2 πk

Adicionar

x

a ambos os lados

13 \cdot \frac{n}{2} - x + x = π + arcsin (- 1 + sin (x)) + 2 πk + x

Simplificar

13 \cdot \frac{n}{2} = π + arcsin (- 1 + sin (x)) + 2 πk + x

13 \cdot \frac{n}{2} = π + arcsin (- 1 + sin (x)) + 2 πk + x

Simplificar

13 \cdot \frac{n}{2} : \frac{13 n}{2}

13 \cdot \frac{n}{2}

Multiplicar frações:

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

= \frac{n \cdot 13}{2}

\frac{13 n}{2} = π + arcsin (- 1 + sin (x)) + 2 πk + x

Multiplicar ambos os lados por

2

\frac{13 n}{2} = π + arcsin (- 1 + sin (x)) + 2 πk + x

Multiplicar ambos os lados por

2

\frac{13 n}{2} \cdot 2 = π 2 + arcsin (- 1 + sin (x)) \cdot 2 + 2 πk \cdot 2 + x \cdot 2

Simplificar

\frac{13 n}{2} \cdot 2 = π 2 + arcsin (- 1 + sin (x)) \cdot 2 + 2 πk \cdot 2 + x \cdot 2

Simplificar

\frac{13 n}{2} \cdot 2 : 13 n

\frac{13 n}{2} \cdot 2

Multiplicar frações:

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

= \frac{13 n \cdot 2}{2}

Eliminar o fator comum:

2

= 13 n

Simplificar

π 2 : 2 π

π 2

Aplique a regra comutativa:

π 2 = 2 π

2 π

Simplificar

arcsin (- 1 + sin (x)) \cdot 2 : 2 arcsin (- 1 + sin (x))

arcsin (- 1 + sin (x)) \cdot 2

Aplique a regra comutativa:

arcsin (- 1 + sin (x)) \cdot 2 = 2 arcsin (- 1 + sin (x))

2 arcsin (- 1 + sin (x))

Simplificar

2 πk \cdot 2 : 4 πk

2 πk \cdot 2

Multiplicar os números:

2 \cdot 2 = 4

= 4 πk

Simplificar

x \cdot 2 : 2 x

x \cdot 2

Aplique a regra comutativa:

x \cdot 2 = 2 x

2 x

13 n = 2 π + 2 arcsin (- 1 + sin (x)) + 4 πk + 2 x

13 n = 2 π + 2 arcsin (- 1 + sin (x)) + 4 πk + 2 x

13 n = 2 π + 2 arcsin (- 1 + sin (x)) + 4 πk + 2 x

Dividir ambos os lados por

13

13 n = 2 π + 2 arcsin (- 1 + sin (x)) + 4 πk + 2 x

Dividir ambos os lados por

13

\frac{13 n}{13} = \frac{2 π}{13} + \frac{2 arcsin ( - 1 + sin ( x ) )}{13} + \frac{4 πk}{13} + \frac{2 x}{13}

Simplificar

n = \frac{2 π}{13} + \frac{2 arcsin ( - 1 + sin ( x ) )}{13} + \frac{4 πk}{13} + \frac{2 x}{13}

n = \frac{2 π}{13} + \frac{2 arcsin ( - 1 + sin ( x ) )}{13} + \frac{4 πk}{13} + \frac{2 x}{13}

n = \frac{2 arcsin ( 1 - sin ( x ) )}{13} + \frac{4 πk}{13} + \frac{2 x}{13}, n = \frac{2 π}{13} + \frac{2 arcsin ( - 1 + sin ( x ) )}{13} + \frac{4 πk}{13} + \frac{2 x}{13}

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