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0.175=0.34sin(93.4x)

Solución

0.175 = 0.34 sin (93.4 x)

x = \frac{0.54066 \dots}{93.4} + \frac{2 πn}{93.4}, x = \frac{π}{93.4} - \frac{0.54066 \dots}{93.4} + \frac{2 πn}{93.4}

Grados

x = 0.33166 \dots^{\circ} + 3.85438 \dots^{\circ} n, x = 1.59552 \dots^{\circ} + 3.85438 \dots^{\circ} n

Pasos de solución

0.175 = 0.34 sin (93.4 x)

Intercambiar lados

0.34 sin (93.4 x) = 0.175

Multiplicar ambos lados por

1000

0.34 sin (93.4 x) = 0.175

Para eliminar los puntos decimales, multiplique por 10 por cada digito después del punto decimalHay digitos

3

a la derecha del punto decimal, por lo que debe multiplicar por

1000

0.34 sin (93.4 x) \cdot 1000 = 0.175 \cdot 1000

Simplificar

340 sin (93.4 x) = 175

340 sin (93.4 x) = 175

Dividir ambos lados entre

340

340 sin (93.4 x) = 175

Dividir ambos lados entre

340

\frac{340 sin ( 93.4 x )}{340} = \frac{175}{340}

Simplificar

sin (93.4 x) = \frac{35}{68}

sin (93.4 x) = \frac{35}{68}

Aplicar propiedades trigonométricas inversas

sin (93.4 x) = \frac{35}{68}

Soluciones generales para

sin (93.4 x) = \frac{35}{68}

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

93.4 x = arcsin (\frac{35}{68}) + 2 πn, 93.4 x = π - arcsin (\frac{35}{68}) + 2 πn

93.4 x = arcsin (\frac{35}{68}) + 2 πn, 93.4 x = π - arcsin (\frac{35}{68}) + 2 πn

Resolver

93.4 x = arcsin (\frac{35}{68}) + 2 πn : x = \frac{arcsin ( \frac{35}{68} )}{93.4} + \frac{2 πn}{93.4}

93.4 x = arcsin (\frac{35}{68}) + 2 πn

Dividir ambos lados entre

93.4

93.4 x = arcsin (\frac{35}{68}) + 2 πn

Dividir ambos lados entre

93.4

\frac{93.4 x}{93.4} = \frac{arcsin ( \frac{35}{68} )}{93.4} + \frac{2 πn}{93.4}

Simplificar

x = \frac{arcsin ( \frac{35}{68} )}{93.4} + \frac{2 πn}{93.4}

x = \frac{arcsin ( \frac{35}{68} )}{93.4} + \frac{2 πn}{93.4}

Resolver

93.4 x = π - arcsin (\frac{35}{68}) + 2 πn : x = \frac{π}{93.4} - \frac{arcsin ( \frac{35}{68} )}{93.4} + \frac{2 πn}{93.4}

93.4 x = π - arcsin (\frac{35}{68}) + 2 πn

Dividir ambos lados entre

93.4

93.4 x = π - arcsin (\frac{35}{68}) + 2 πn

Dividir ambos lados entre

93.4

\frac{93.4 x}{93.4} = \frac{π}{93.4} - \frac{arcsin ( \frac{35}{68} )}{93.4} + \frac{2 πn}{93.4}

Simplificar

x = \frac{π}{93.4} - \frac{arcsin ( \frac{35}{68} )}{93.4} + \frac{2 πn}{93.4}

x = \frac{π}{93.4} - \frac{arcsin ( \frac{35}{68} )}{93.4} + \frac{2 πn}{93.4}

x = \frac{arcsin ( \frac{35}{68} )}{93.4} + \frac{2 πn}{93.4}, x = \frac{π}{93.4} - \frac{arcsin ( \frac{35}{68} )}{93.4} + \frac{2 πn}{93.4}

Mostrar soluciones en forma decimal

x = \frac{0.54066 \dots}{93.4} + \frac{2 πn}{93.4}, x = \frac{π}{93.4} - \frac{0.54066 \dots}{93.4} + \frac{2 πn}{93.4}