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Popular Trigonometría >

120=23sin(pi/6 (x))+107

Solución

120 = 23 sin (\frac{π}{6} (x)) + 107

Solución

x = \frac{6 \cdot 0.60069 \dots}{π} + 12 n, x = 6 - \frac{6 \cdot 0.60069 \dots}{π} + 12 n

Grados

x = 65.73237 \dots^{\circ} + 687.54935 \dots^{\circ} n, x = 278.04230 \dots^{\circ} + 687.54935 \dots^{\circ} n

Pasos de solución

120 = 23 sin (\frac{π}{6} (x)) + 107

Intercambiar lados

23 sin (\frac{π}{6} x) + 107 = 120

Desplace

107

a la derecha

23 sin (\frac{π}{6} x) + 107 = 120

Restar

107

de ambos lados

23 sin (\frac{π}{6} x) + 107 - 107 = 120 - 107

Simplificar

23 sin (\frac{π}{6} x) = 13

23 sin (\frac{π}{6} x) = 13

Dividir ambos lados entre

23

23 sin (\frac{π}{6} x) = 13

Dividir ambos lados entre

23

\frac{23 sin ( \frac{π}{6} x )}{23} = \frac{13}{23}

Simplificar

sin (\frac{π}{6} x) = \frac{13}{23}

sin (\frac{π}{6} x) = \frac{13}{23}

Aplicar propiedades trigonométricas inversas

sin (\frac{π}{6} x) = \frac{13}{23}

Soluciones generales para

sin (\frac{π}{6} x) = \frac{13}{23}

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

\frac{π}{6} x = arcsin (\frac{13}{23}) + 2 πn, \frac{π}{6} x = π - arcsin (\frac{13}{23}) + 2 πn

\frac{π}{6} x = arcsin (\frac{13}{23}) + 2 πn, \frac{π}{6} x = π - arcsin (\frac{13}{23}) + 2 πn

Resolver

\frac{π}{6} x = arcsin (\frac{13}{23}) + 2 πn : x = \frac{6 arcsin ( \frac{13}{23} )}{π} + 12 n

\frac{π}{6} x = arcsin (\frac{13}{23}) + 2 πn

Multiplicar ambos lados por

6

\frac{π}{6} x = arcsin (\frac{13}{23}) + 2 πn

Multiplicar ambos lados por

6

6 \cdot \frac{π}{6} x = 6 arcsin (\frac{13}{23}) + 6 \cdot 2 πn

Simplificar

6 \cdot \frac{π}{6} x = 6 arcsin (\frac{13}{23}) + 6 \cdot 2 πn

Simplificar

6 \cdot \frac{π}{6} x : π x

6 \cdot \frac{π}{6} x

Multiplicar fracciones:

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

= \frac{6 π}{6} x

Eliminar los terminos comunes:

6

= x π

Simplificar

6 arcsin (\frac{13}{23}) + 6 \cdot 2 πn : 6 arcsin (\frac{13}{23}) + 12 πn

6 arcsin (\frac{13}{23}) + 6 \cdot 2 πn

Multiplicar los numeros:

6 \cdot 2 = 12

= 6 arcsin (\frac{13}{23}) + 12 πn

π x = 6 arcsin (\frac{13}{23}) + 12 πn

π x = 6 arcsin (\frac{13}{23}) + 12 πn

π x = 6 arcsin (\frac{13}{23}) + 12 πn

Dividir ambos lados entre

π

π x = 6 arcsin (\frac{13}{23}) + 12 πn

Dividir ambos lados entre

π

\frac{π x}{π} = \frac{6 arcsin ( \frac{13}{23} )}{π} + \frac{12 πn}{π}

Simplificar

x = \frac{6 arcsin ( \frac{13}{23} )}{π} + 12 n

x = \frac{6 arcsin ( \frac{13}{23} )}{π} + 12 n

Resolver

\frac{π}{6} x = π - arcsin (\frac{13}{23}) + 2 πn : x = 6 - \frac{6 arcsin ( \frac{13}{23} )}{π} + 12 n

\frac{π}{6} x = π - arcsin (\frac{13}{23}) + 2 πn

Multiplicar ambos lados por

6

\frac{π}{6} x = π - arcsin (\frac{13}{23}) + 2 πn

Multiplicar ambos lados por

6

6 \cdot \frac{π}{6} x = 6 π - 6 arcsin (\frac{13}{23}) + 6 \cdot 2 πn

Simplificar

6 \cdot \frac{π}{6} x = 6 π - 6 arcsin (\frac{13}{23}) + 6 \cdot 2 πn

Simplificar

6 \cdot \frac{π}{6} x : π x

6 \cdot \frac{π}{6} x

Multiplicar fracciones:

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

= \frac{6 π}{6} x

Eliminar los terminos comunes:

6

= x π

Simplificar

6 π - 6 arcsin (\frac{13}{23}) + 6 \cdot 2 πn : 6 π - 6 arcsin (\frac{13}{23}) + 12 πn

6 π - 6 arcsin (\frac{13}{23}) + 6 \cdot 2 πn

Multiplicar los numeros:

6 \cdot 2 = 12

= 6 π - 6 arcsin (\frac{13}{23}) + 12 πn

π x = 6 π - 6 arcsin (\frac{13}{23}) + 12 πn

π x = 6 π - 6 arcsin (\frac{13}{23}) + 12 πn

π x = 6 π - 6 arcsin (\frac{13}{23}) + 12 πn

Dividir ambos lados entre

π

π x = 6 π - 6 arcsin (\frac{13}{23}) + 12 πn

Dividir ambos lados entre

π

\frac{π x}{π} = \frac{6 π}{π} - \frac{6 arcsin ( \frac{13}{23} )}{π} + \frac{12 πn}{π}

Simplificar

\frac{π x}{π} = \frac{6 π}{π} - \frac{6 arcsin ( \frac{13}{23} )}{π} + \frac{12 πn}{π}

Simplificar

\frac{π x}{π} : x

\frac{π x}{π}

Eliminar los terminos comunes:

π

= x

Simplificar

\frac{6 π}{π} - \frac{6 arcsin ( \frac{13}{23} )}{π} + \frac{12 πn}{π} : 6 - \frac{6 arcsin ( \frac{13}{23} )}{π} + 12 n

\frac{6 π}{π} - \frac{6 arcsin ( \frac{13}{23} )}{π} + \frac{12 πn}{π}

Cancelar

\frac{6 π}{π} : 6

\frac{6 π}{π}

Eliminar los terminos comunes:

π

= 6

= 6 - \frac{6 arcsin ( \frac{13}{23} )}{π} + \frac{12 πn}{π}

Cancelar

\frac{12 πn}{π} : 12 n

\frac{12 πn}{π}

Eliminar los terminos comunes:

π

= 12 n

= 6 - \frac{6 arcsin ( \frac{13}{23} )}{π} + 12 n

x = 6 - \frac{6 arcsin ( \frac{13}{23} )}{π} + 12 n

x = 6 - \frac{6 arcsin ( \frac{13}{23} )}{π} + 12 n

x = 6 - \frac{6 arcsin ( \frac{13}{23} )}{π} + 12 n

x = \frac{6 arcsin ( \frac{13}{23} )}{π} + 12 n, x = 6 - \frac{6 arcsin ( \frac{13}{23} )}{π} + 12 n

Mostrar soluciones en forma decimal

x = \frac{6 \cdot 0.60069 \dots}{π} + 12 n, x = 6 - \frac{6 \cdot 0.60069 \dots}{π} + 12 n

Gráfica

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