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Popular Trigonometría >

15=10sin(pi/(20)(x+10))+12

Solución

15 = 10 sin (\frac{π}{20} (x + 10)) + 12

Solución

x = \frac{20 \cdot 0.30469 \dots}{π} + 40 n - 10, x = 40 n + 10 - \frac{20 \cdot 0.30469 \dots}{π}

Grados

x = - 461.81924 \dots^{\circ} + 2291.83118 \dots^{\circ} n, x = 461.81924 \dots^{\circ} + 2291.83118 \dots^{\circ} n

Pasos de solución

15 = 10 sin (\frac{π}{20} (x + 10)) + 12

Intercambiar lados

10 sin (\frac{π}{20} (x + 10)) + 12 = 15

Desplace

12

a la derecha

10 sin (\frac{π}{20} (x + 10)) + 12 = 15

Restar

12

de ambos lados

10 sin (\frac{π}{20} (x + 10)) + 12 - 12 = 15 - 12

Simplificar

10 sin (\frac{π}{20} (x + 10)) = 3

10 sin (\frac{π}{20} (x + 10)) = 3

Dividir ambos lados entre

10

10 sin (\frac{π}{20} (x + 10)) = 3

Dividir ambos lados entre

10

\frac{10 sin ( \frac{π}{20} ( x + 10 ) )}{10} = \frac{3}{10}

Simplificar

sin (\frac{π}{20} (x + 10)) = \frac{3}{10}

sin (\frac{π}{20} (x + 10)) = \frac{3}{10}

Aplicar propiedades trigonométricas inversas

sin (\frac{π}{20} (x + 10)) = \frac{3}{10}

Soluciones generales para

sin (\frac{π}{20} (x + 10)) = \frac{3}{10}

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

\frac{π}{20} (x + 10) = arcsin (\frac{3}{10}) + 2 πn, \frac{π}{20} (x + 10) = π - arcsin (\frac{3}{10}) + 2 πn

\frac{π}{20} (x + 10) = arcsin (\frac{3}{10}) + 2 πn, \frac{π}{20} (x + 10) = π - arcsin (\frac{3}{10}) + 2 πn

Resolver

\frac{π}{20} (x + 10) = arcsin (\frac{3}{10}) + 2 πn : x = \frac{20 arcsin ( \frac{3}{10} )}{π} + 40 n - 10

\frac{π}{20} (x + 10) = arcsin (\frac{3}{10}) + 2 πn

Multiplicar ambos lados por

20

\frac{π}{20} (x + 10) = arcsin (\frac{3}{10}) + 2 πn

Multiplicar ambos lados por

20

20 \cdot \frac{π}{20} (x + 10) = 20 arcsin (\frac{3}{10}) + 20 \cdot 2 πn

Simplificar

20 \cdot \frac{π}{20} (x + 10) = 20 arcsin (\frac{3}{10}) + 20 \cdot 2 πn

Simplificar

20 \cdot \frac{π}{20} (x + 10) : π (x + 10)

20 \cdot \frac{π}{20} (x + 10)

Multiplicar fracciones:

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

= \frac{20 π}{20} (x + 10)

Eliminar los terminos comunes:

20

= (x + 10) π

Simplificar

20 arcsin (\frac{3}{10}) + 20 \cdot 2 πn : 20 arcsin (\frac{3}{10}) + 40 πn

20 arcsin (\frac{3}{10}) + 20 \cdot 2 πn

Multiplicar los numeros:

20 \cdot 2 = 40

= 20 arcsin (\frac{3}{10}) + 40 πn

π (x + 10) = 20 arcsin (\frac{3}{10}) + 40 πn

π (x + 10) = 20 arcsin (\frac{3}{10}) + 40 πn

π (x + 10) = 20 arcsin (\frac{3}{10}) + 40 πn

Dividir ambos lados entre

π

π (x + 10) = 20 arcsin (\frac{3}{10}) + 40 πn

Dividir ambos lados entre

π

\frac{π ( x + 10 )}{π} = \frac{20 arcsin ( \frac{3}{10} )}{π} + \frac{40 πn}{π}

Simplificar

x + 10 = \frac{20 arcsin ( \frac{3}{10} )}{π} + 40 n

x + 10 = \frac{20 arcsin ( \frac{3}{10} )}{π} + 40 n

Desplace

10

a la derecha

x + 10 = \frac{20 arcsin ( \frac{3}{10} )}{π} + 40 n

Restar

10

de ambos lados

x + 10 - 10 = \frac{20 arcsin ( \frac{3}{10} )}{π} + 40 n - 10

Simplificar

x = \frac{20 arcsin ( \frac{3}{10} )}{π} + 40 n - 10

x = \frac{20 arcsin ( \frac{3}{10} )}{π} + 40 n - 10

Resolver

\frac{π}{20} (x + 10) = π - arcsin (\frac{3}{10}) + 2 πn : x = 40 n + 10 - \frac{20 arcsin ( \frac{3}{10} )}{π}

\frac{π}{20} (x + 10) = π - arcsin (\frac{3}{10}) + 2 πn

Multiplicar ambos lados por

20

\frac{π}{20} (x + 10) = π - arcsin (\frac{3}{10}) + 2 πn

Multiplicar ambos lados por

20

20 \cdot \frac{π}{20} (x + 10) = 20 π - 20 arcsin (\frac{3}{10}) + 20 \cdot 2 πn

Simplificar

20 \cdot \frac{π}{20} (x + 10) = 20 π - 20 arcsin (\frac{3}{10}) + 20 \cdot 2 πn

Simplificar

20 \cdot \frac{π}{20} (x + 10) : π (x + 10)

20 \cdot \frac{π}{20} (x + 10)

Multiplicar fracciones:

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

= \frac{20 π}{20} (x + 10)

Eliminar los terminos comunes:

20

= (x + 10) π

Simplificar

20 π - 20 arcsin (\frac{3}{10}) + 20 \cdot 2 πn : 20 π - 20 arcsin (\frac{3}{10}) + 40 πn

20 π - 20 arcsin (\frac{3}{10}) + 20 \cdot 2 πn

Multiplicar los numeros:

20 \cdot 2 = 40

= 20 π - 20 arcsin (\frac{3}{10}) + 40 πn

π (x + 10) = 20 π - 20 arcsin (\frac{3}{10}) + 40 πn

π (x + 10) = 20 π - 20 arcsin (\frac{3}{10}) + 40 πn

π (x + 10) = 20 π - 20 arcsin (\frac{3}{10}) + 40 πn

Dividir ambos lados entre

π

π (x + 10) = 20 π - 20 arcsin (\frac{3}{10}) + 40 πn

Dividir ambos lados entre

π

\frac{π ( x + 10 )}{π} = \frac{20 π}{π} - \frac{20 arcsin ( \frac{3}{10} )}{π} + \frac{40 πn}{π}

Simplificar

\frac{π ( x + 10 )}{π} = \frac{20 π}{π} - \frac{20 arcsin ( \frac{3}{10} )}{π} + \frac{40 πn}{π}

Simplificar

\frac{π ( x + 10 )}{π} : x + 10

\frac{π ( x + 10 )}{π}

Eliminar los terminos comunes:

π

= x + 10

Simplificar

\frac{20 π}{π} - \frac{20 arcsin ( \frac{3}{10} )}{π} + \frac{40 πn}{π} : 20 - \frac{20 arcsin ( \frac{3}{10} )}{π} + 40 n

\frac{20 π}{π} - \frac{20 arcsin ( \frac{3}{10} )}{π} + \frac{40 πn}{π}

Cancelar

\frac{20 π}{π} : 20

\frac{20 π}{π}

Eliminar los terminos comunes:

π

= 20

= 20 - \frac{20 arcsin ( \frac{3}{10} )}{π} + \frac{40 πn}{π}

Cancelar

\frac{40 πn}{π} : 40 n

\frac{40 πn}{π}

Eliminar los terminos comunes:

π

= 40 n

= 20 - \frac{20 arcsin ( \frac{3}{10} )}{π} + 40 n

x + 10 = 20 - \frac{20 arcsin ( \frac{3}{10} )}{π} + 40 n

x + 10 = 20 - \frac{20 arcsin ( \frac{3}{10} )}{π} + 40 n

x + 10 = 20 - \frac{20 arcsin ( \frac{3}{10} )}{π} + 40 n

Desplace

10

a la derecha

x + 10 = 20 - \frac{20 arcsin ( \frac{3}{10} )}{π} + 40 n

Restar

10

de ambos lados

x + 10 - 10 = 20 - \frac{20 arcsin ( \frac{3}{10} )}{π} + 40 n - 10

Simplificar

x + 10 - 10 = 20 - \frac{20 arcsin ( \frac{3}{10} )}{π} + 40 n - 10

Simplificar

x + 10 - 10 : x

x + 10 - 10

Sumar elementos similares:

10 - 10 = 0

= x

Simplificar

20 - \frac{20 arcsin ( \frac{3}{10} )}{π} + 40 n - 10 : 40 n + 10 - \frac{20 arcsin ( \frac{3}{10} )}{π}

20 - \frac{20 arcsin ( \frac{3}{10} )}{π} + 40 n - 10

Restar:

20 - 10 = 10

= 40 n + 10 - \frac{20 arcsin ( \frac{3}{10} )}{π}

x = 40 n + 10 - \frac{20 arcsin ( \frac{3}{10} )}{π}

x = 40 n + 10 - \frac{20 arcsin ( \frac{3}{10} )}{π}

x = 40 n + 10 - \frac{20 arcsin ( \frac{3}{10} )}{π}

x = \frac{20 arcsin ( \frac{3}{10} )}{π} + 40 n - 10, x = 40 n + 10 - \frac{20 arcsin ( \frac{3}{10} )}{π}

Mostrar soluciones en forma decimal

x = \frac{20 \cdot 0.30469 \dots}{π} + 40 n - 10, x = 40 n + 10 - \frac{20 \cdot 0.30469 \dots}{π}

Gráfica

Ejemplos populares

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