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-0.002=sin(2pi*(3)-500pi(0)+x)

Solución

- 0.002 = sin (2 π \cdot (3) - 500 π (0) + x)

x = - 0.00200 \dots + 2 πn - 6 π, x = - 5 π + 2 πn + 0.00200 \dots

Grados

x = - 1080.11459 \dots^{\circ} + 36 0^{\circ} n, x = - 899.88540 \dots^{\circ} + 36 0^{\circ} n

Pasos de solución

- 0.002 = sin (2 π (3) - 500 π (0) + x)

Intercambiar lados

sin (2 π 3 - 500 π 0 + x) = - 0.002

Aplicar propiedades trigonométricas inversas

sin (2 π 3 - 500 π 0 + x) = - 0.002

Soluciones generales para

sin (2 π 3 - 500 π 0 + x) = - 0.002

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

2 π 3 - 500 π 0 + x = arcsin (- 0.002) + 2 πn, 2 π 3 - 500 π 0 + x = π + arcsin (0.002) + 2 πn

2 π 3 - 500 π 0 + x = arcsin (- 0.002) + 2 πn, 2 π 3 - 500 π 0 + x = π + arcsin (0.002) + 2 πn

Resolver

2 π 3 - 500 π 0 + x = arcsin (- 0.002) + 2 πn : x = - arcsin (\frac{1}{500}) + 2 πn - 6 π

2 π 3 - 500 π 0 + x = arcsin (- 0.002) + 2 πn

Simplificar

2 π 3 - 500 π 0 + x : x + 6 π

2 π 3 - 500 π 0 + x

Multiplicar los numeros:

2 \cdot 3 = 6

= 6 π - 500 \cdot 0 π + x

Aplicar la regla

0 \cdot a = 0

= 6 π - 0 + x

6 π - 0 + x = 6 π + x

= x + 6 π

Simplificar

arcsin (- 0.002) + 2 πn : - arcsin (\frac{1}{500}) + 2 πn

arcsin (- 0.002) + 2 πn

arcsin (- 0.002) = - arcsin (\frac{1}{500})

arcsin (- 0.002)

= arcsin (- \frac{1}{500})

Utilizar la siguiente propiedad:

arcsin (- x) = - arcsin (x)

arcsin (- \frac{1}{500}) = - arcsin (\frac{1}{500})

= - arcsin (\frac{1}{500})

= - arcsin (\frac{1}{500}) + 2 πn

x + 6 π = - arcsin (\frac{1}{500}) + 2 πn

Desplace

6 π

a la derecha

x + 6 π = - arcsin (\frac{1}{500}) + 2 πn

Restar

6 π

de ambos lados

x + 6 π - 6 π = - arcsin (\frac{1}{500}) + 2 πn - 6 π

Simplificar

x = - arcsin (\frac{1}{500}) + 2 πn - 6 π

x = - arcsin (\frac{1}{500}) + 2 πn - 6 π

Resolver

2 π 3 - 500 π 0 + x = π + arcsin (0.002) + 2 πn : x = - 5 π + 2 πn + arcsin (0.002)

2 π 3 - 500 π 0 + x = π + arcsin (0.002) + 2 πn

Multiplicar los numeros:

2 \cdot 3 = 6

6 π - 500 \cdot 0 π + x = π + arcsin (0.002) + 2 πn

Aplicar la regla

0 \cdot a = 0

6 π - 0 + x = π + arcsin (0.002) + 2 πn

6 π - 0 + x = 6 π + x

x + 6 π = π + arcsin (0.002) + 2 πn

Desplace

6 π

a la derecha

x + 6 π = π + arcsin (0.002) + 2 πn

Restar

6 π

de ambos lados

x + 6 π - 6 π = π + arcsin (0.002) + 2 πn - 6 π

Simplificar

x = - 5 π + 2 πn + arcsin (0.002)

x = - 5 π + 2 πn + arcsin (0.002)

x = - arcsin (\frac{1}{500}) + 2 πn - 6 π, x = - 5 π + 2 πn + arcsin (0.002)

Mostrar soluciones en forma decimal

x = - 0.00200 \dots + 2 πn - 6 π, x = - 5 π + 2 πn + 0.00200 \dots