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200.4=200+sin(x/(240))

Solución

200.4 = 200 + sin (\frac{x}{240})

x = 240 \cdot 0.41151 \dots + 480 πn, x = 240 π - 240 \cdot 0.41151 \dots + 480 πn

Grados

x = 5658.76283 \dots^{\circ} + 86399.99999 \dots^{\circ} n, x = 37541.23716 \dots^{\circ} + 86399.99999 \dots^{\circ} n

Pasos de solución

200.4 = 200 + sin (\frac{x}{240})

Intercambiar lados

200 + sin (\frac{x}{240}) = 200.4

Desplace

200

a la derecha

200 + sin (\frac{x}{240}) = 200.4

Restar

200

de ambos lados

200 + sin (\frac{x}{240}) - 200 = 200.4 - 200

Simplificar

sin (\frac{x}{240}) = 0.4

sin (\frac{x}{240}) = 0.4

Aplicar propiedades trigonométricas inversas

sin (\frac{x}{240}) = 0.4

Soluciones generales para

sin (\frac{x}{240}) = 0.4

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

\frac{x}{240} = arcsin (0.4) + 2 πn, \frac{x}{240} = π - arcsin (0.4) + 2 πn

\frac{x}{240} = arcsin (0.4) + 2 πn, \frac{x}{240} = π - arcsin (0.4) + 2 πn

Resolver

\frac{x}{240} = arcsin (0.4) + 2 πn : x = 240 arcsin (0.4) + 480 πn

\frac{x}{240} = arcsin (0.4) + 2 πn

Multiplicar ambos lados por

240

\frac{x}{240} = arcsin (0.4) + 2 πn

Multiplicar ambos lados por

240

\frac{240 x}{240} = 240 arcsin (0.4) + 240 \cdot 2 πn

Simplificar

x = 240 arcsin (0.4) + 480 πn

x = 240 arcsin (0.4) + 480 πn

Resolver

\frac{x}{240} = π - arcsin (0.4) + 2 πn : x = 240 π - 240 arcsin (0.4) + 480 πn

\frac{x}{240} = π - arcsin (0.4) + 2 πn

Multiplicar ambos lados por

240

\frac{x}{240} = π - arcsin (0.4) + 2 πn

Multiplicar ambos lados por

240

\frac{240 x}{240} = 240 π - 240 arcsin (0.4) + 240 \cdot 2 πn

Simplificar

x = 240 π - 240 arcsin (0.4) + 480 πn

x = 240 π - 240 arcsin (0.4) + 480 πn

x = 240 arcsin (0.4) + 480 πn, x = 240 π - 240 arcsin (0.4) + 480 πn

Mostrar soluciones en forma decimal

x = 240 \cdot 0.41151 \dots + 480 πn, x = 240 π - 240 \cdot 0.41151 \dots + 480 πn