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17sin(θ+61.9)=k

Solución

17 sin (θ + 61. 9^{\circ}) = k

Solución

θ = arcsin (\frac{k}{17}) + 36 0^{\circ} n - 61. 9^{\circ}, θ = 18 0^{\circ} + arcsin (- \frac{k}{17}) + 36 0^{\circ} n - 61. 9^{\circ}

+1

radianes

θ = arcsin (\frac{k}{17}) - \frac{619 π}{1800} + 2 πn, θ = π + arcsin (- \frac{k}{17}) - \frac{619 π}{1800} + 2 πn

Pasos de solución

17 sin (θ + 61. 9^{\circ}) = k

Dividir ambos lados entre

17

17 sin (θ + 61. 9^{\circ}) = k

Dividir ambos lados entre

17

\frac{17 sin ( θ + 61. 9 ^{\circ} )}{17} = \frac{k}{17}

Simplificar

sin (θ + 61. 9^{\circ}) = \frac{k}{17}

sin (θ + 61. 9^{\circ}) = \frac{k}{17}

Aplicar propiedades trigonométricas inversas

sin (θ + 61. 9^{\circ}) = \frac{k}{17}

Soluciones generales para

sin (θ + 61. 9^{\circ}) = \frac{k}{17}

sin (x) = a \Rightarrow x = arcsin (a) + 36 0^{\circ} n, x = 18 0^{\circ} + arcsin (a) + 36 0^{\circ} n

θ + 61. 9^{\circ} = arcsin (\frac{k}{17}) + 36 0^{\circ} n, θ + 61. 9^{\circ} = 18 0^{\circ} + arcsin (- \frac{k}{17}) + 36 0^{\circ} n

θ + 61. 9^{\circ} = arcsin (\frac{k}{17}) + 36 0^{\circ} n, θ + 61. 9^{\circ} = 18 0^{\circ} + arcsin (- \frac{k}{17}) + 36 0^{\circ} n

Resolver

θ + 61. 9^{\circ} = arcsin (\frac{k}{17}) + 36 0^{\circ} n : θ = arcsin (\frac{k}{17}) + 36 0^{\circ} n - 61. 9^{\circ}

θ + 61. 9^{\circ} = arcsin (\frac{k}{17}) + 36 0^{\circ} n

Desplace

61. 9^{\circ}

a la derecha

θ + 61. 9^{\circ} = arcsin (\frac{k}{17}) + 36 0^{\circ} n

Restar

61. 9^{\circ}

de ambos lados

θ + 61. 9^{\circ} - 61. 9^{\circ} = arcsin (\frac{k}{17}) + 36 0^{\circ} n - 61. 9^{\circ}

Simplificar

θ = arcsin (\frac{k}{17}) + 36 0^{\circ} n - 61. 9^{\circ}

θ = arcsin (\frac{k}{17}) + 36 0^{\circ} n - 61. 9^{\circ}

Resolver

θ + 61. 9^{\circ} = 18 0^{\circ} + arcsin (- \frac{k}{17}) + 36 0^{\circ} n : θ = 18 0^{\circ} + arcsin (- \frac{k}{17}) + 36 0^{\circ} n - 61. 9^{\circ}

θ + 61. 9^{\circ} = 18 0^{\circ} + arcsin (- \frac{k}{17}) + 36 0^{\circ} n

Desplace

61. 9^{\circ}

a la derecha

θ + 61. 9^{\circ} = 18 0^{\circ} + arcsin (- \frac{k}{17}) + 36 0^{\circ} n

Restar

61. 9^{\circ}

de ambos lados

θ + 61. 9^{\circ} - 61. 9^{\circ} = 18 0^{\circ} + arcsin (- \frac{k}{17}) + 36 0^{\circ} n - 61. 9^{\circ}

Simplificar

θ = 18 0^{\circ} + arcsin (- \frac{k}{17}) + 36 0^{\circ} n - 61. 9^{\circ}

θ = 18 0^{\circ} + arcsin (- \frac{k}{17}) + 36 0^{\circ} n - 61. 9^{\circ}

θ = arcsin (\frac{k}{17}) + 36 0^{\circ} n - 61. 9^{\circ}, θ = 18 0^{\circ} + arcsin (- \frac{k}{17}) + 36 0^{\circ} n - 61. 9^{\circ}

Gráfica

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