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Popular Trigonometría >

20=2.891sin(0.016d-1.183)+18.512

Solución

20 = 2.891 sin (0.016 d - 1.183) + 18.512

Solución

d = \frac{0.54065 \dots}{0.016} + \frac{2 πn}{0.016} + \frac{1.183}{0.016}, d = \frac{π}{0.016} - \frac{0.54065 \dots}{0.016} + \frac{2 πn}{0.016} + \frac{1.183}{0.016}

Grados

d = 6172.39781 \dots^{\circ} + 2250 0^{\circ} n, d = 13550.21558 \dots^{\circ} + 2250 0^{\circ} n

Pasos de solución

20 = 2.891 sin (0.016 d - 1.183) + 18.512

Intercambiar lados

2.891 sin (0.016 d - 1.183) + 18.512 = 20

Multiplicar ambos lados por

1000

2.891 sin (0.016 d - 1.183) + 18.512 = 20

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

2.891 sin (0.016 d - 1.183) \cdot 1000 + 18.512 \cdot 1000 = 20 \cdot 1000

Simplificar

2891 sin (0.016 d - 1.183) + 18512 = 20000

2891 sin (0.016 d - 1.183) + 18512 = 20000

Desplace

18512

a la derecha

2891 sin (0.016 d - 1.183) + 18512 = 20000

Restar

18512

de ambos lados

2891 sin (0.016 d - 1.183) + 18512 - 18512 = 20000 - 18512

Simplificar

2891 sin (0.016 d - 1.183) = 1488

2891 sin (0.016 d - 1.183) = 1488

Dividir ambos lados entre

2891

2891 sin (0.016 d - 1.183) = 1488

Dividir ambos lados entre

2891

\frac{2891 sin ( 0.016 d - 1.183 )}{2891} = \frac{1488}{2891}

Simplificar

sin (0.016 d - 1.183) = \frac{1488}{2891}

sin (0.016 d - 1.183) = \frac{1488}{2891}

Aplicar propiedades trigonométricas inversas

sin (0.016 d - 1.183) = \frac{1488}{2891}

Soluciones generales para

sin (0.016 d - 1.183) = \frac{1488}{2891}

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

0.016 d - 1.183 = arcsin (\frac{1488}{2891}) + 2 πn, 0.016 d - 1.183 = π - arcsin (\frac{1488}{2891}) + 2 πn

0.016 d - 1.183 = arcsin (\frac{1488}{2891}) + 2 πn, 0.016 d - 1.183 = π - arcsin (\frac{1488}{2891}) + 2 πn

Resolver

0.016 d - 1.183 = arcsin (\frac{1488}{2891}) + 2 πn : d = \frac{arcsin ( \frac{1488}{2891} )}{0.016} + \frac{2 πn}{0.016} + \frac{1.183}{0.016}

0.016 d - 1.183 = arcsin (\frac{1488}{2891}) + 2 πn

Desplace

1.183

a la derecha

0.016 d - 1.183 = arcsin (\frac{1488}{2891}) + 2 πn

Sumar

1.183

a ambos lados

0.016 d - 1.183 + 1.183 = arcsin (\frac{1488}{2891}) + 2 πn + 1.183

Simplificar

0.016 d = arcsin (\frac{1488}{2891}) + 2 πn + 1.183

0.016 d = arcsin (\frac{1488}{2891}) + 2 πn + 1.183

Dividir ambos lados entre

0.016

0.016 d = arcsin (\frac{1488}{2891}) + 2 πn + 1.183

Dividir ambos lados entre

0.016

\frac{0.016 d}{0.016} = \frac{arcsin ( \frac{1488}{2891} )}{0.016} + \frac{2 πn}{0.016} + \frac{1.183}{0.016}

Simplificar

d = \frac{arcsin ( \frac{1488}{2891} )}{0.016} + \frac{2 πn}{0.016} + \frac{1.183}{0.016}

d = \frac{arcsin ( \frac{1488}{2891} )}{0.016} + \frac{2 πn}{0.016} + \frac{1.183}{0.016}

Resolver

0.016 d - 1.183 = π - arcsin (\frac{1488}{2891}) + 2 πn : d = \frac{π}{0.016} - \frac{arcsin ( \frac{1488}{2891} )}{0.016} + \frac{2 πn}{0.016} + \frac{1.183}{0.016}

0.016 d - 1.183 = π - arcsin (\frac{1488}{2891}) + 2 πn

Desplace

1.183

a la derecha

0.016 d - 1.183 = π - arcsin (\frac{1488}{2891}) + 2 πn

Sumar

1.183

a ambos lados

0.016 d - 1.183 + 1.183 = π - arcsin (\frac{1488}{2891}) + 2 πn + 1.183

Simplificar

0.016 d = π - arcsin (\frac{1488}{2891}) + 2 πn + 1.183

0.016 d = π - arcsin (\frac{1488}{2891}) + 2 πn + 1.183

Dividir ambos lados entre

0.016

0.016 d = π - arcsin (\frac{1488}{2891}) + 2 πn + 1.183

Dividir ambos lados entre

0.016

\frac{0.016 d}{0.016} = \frac{π}{0.016} - \frac{arcsin ( \frac{1488}{2891} )}{0.016} + \frac{2 πn}{0.016} + \frac{1.183}{0.016}

Simplificar

d = \frac{π}{0.016} - \frac{arcsin ( \frac{1488}{2891} )}{0.016} + \frac{2 πn}{0.016} + \frac{1.183}{0.016}

d = \frac{π}{0.016} - \frac{arcsin ( \frac{1488}{2891} )}{0.016} + \frac{2 πn}{0.016} + \frac{1.183}{0.016}

d = \frac{arcsin ( \frac{1488}{2891} )}{0.016} + \frac{2 πn}{0.016} + \frac{1.183}{0.016}, d = \frac{π}{0.016} - \frac{arcsin ( \frac{1488}{2891} )}{0.016} + \frac{2 πn}{0.016} + \frac{1.183}{0.016}

Mostrar soluciones en forma decimal

d = \frac{0.54065 \dots}{0.016} + \frac{2 πn}{0.016} + \frac{1.183}{0.016}, d = \frac{π}{0.016} - \frac{0.54065 \dots}{0.016} + \frac{2 πn}{0.016} + \frac{1.183}{0.016}

Gráfica

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