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sqrt(5)sin(θ+0.4636)=1

Solución

5 sin (θ + 0.4636) = 1

Solución

θ = 0.46364 \dots + 2 πn - 0.4636, θ = π - 0.46364 \dots + 2 πn - 0.4636

Grados

θ = 0.00272 \dots^{\circ} + 36 0^{\circ} n, θ = 126.87262 \dots^{\circ} + 36 0^{\circ} n

Pasos de solución

5 sin (θ + 0.4636) = 1

Dividir ambos lados entre

5

5 sin (θ + 0.4636) = 1

Dividir ambos lados entre

5

\frac{5 sin ( θ + 0.4636 )}{5} = \frac{1}{5}

Simplificar

\frac{5 sin ( θ + 0.4636 )}{5} = \frac{1}{5}

Simplificar

\frac{5 sin ( θ + 0.4636 )}{5} : sin (θ + 0.4636)

\frac{5 sin ( θ + 0.4636 )}{5}

Eliminar los terminos comunes:

5

= sin (θ + 0.4636)

Simplificar

\frac{1}{5} : \frac{5}{5}

\frac{1}{5}

Multiplicar por el conjugado

\frac{5}{5}

= \frac{1 \cdot 5}{5 5}

1 \cdot 5 = 5

55 = 5

55

Aplicar las leyes de los exponentes:

a a = a

55 = 5

= 5

= \frac{5}{5}

sin (θ + 0.4636) = \frac{5}{5}

sin (θ + 0.4636) = \frac{5}{5}

sin (θ + 0.4636) = \frac{5}{5}

Aplicar propiedades trigonométricas inversas

sin (θ + 0.4636) = \frac{5}{5}

Soluciones generales para

sin (θ + 0.4636) = \frac{5}{5}

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

θ + 0.4636 = arcsin (\frac{5}{5}) + 2 πn, θ + 0.4636 = π - arcsin (\frac{5}{5}) + 2 πn

θ + 0.4636 = arcsin (\frac{5}{5}) + 2 πn, θ + 0.4636 = π - arcsin (\frac{5}{5}) + 2 πn

Resolver

θ + 0.4636 = arcsin (\frac{5}{5}) + 2 πn : θ = arcsin (\frac{1}{5}) + 2 πn - 0.4636

θ + 0.4636 = arcsin (\frac{5}{5}) + 2 πn

Simplificar

arcsin (\frac{5}{5}) + 2 πn : arcsin (\frac{1}{5}) + 2 πn

arcsin (\frac{5}{5}) + 2 πn

\frac{5}{5} = \frac{1}{5}

\frac{5}{5}

Aplicar las leyes de los exponentes:

5 = 5^{\frac{1}{2}}

= \frac{5 ^{\frac{1}{2}}}{5}

Aplicar las leyes de los exponentes:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

\frac{5 ^{\frac{1}{2}}}{5 ^{1}} = \frac{1}{5 ^{1 - \frac{1}{2}}}

= \frac{1}{5 ^{1 - \frac{1}{2}}}

Restar:

1 - \frac{1}{2} = \frac{1}{2}

= \frac{1}{5 ^{\frac{1}{2}}}

Aplicar las leyes de los exponentes:

5^{\frac{1}{2}} = 5

= \frac{1}{5}

= arcsin (\frac{1}{5}) + 2 πn

θ + 0.4636 = arcsin (\frac{1}{5}) + 2 πn

Mover

0.4636

al lado derecho

θ + 0.4636 = arcsin (\frac{1}{5}) + 2 πn

Restar

0.4636

de ambos lados

θ + 0.4636 - 0.4636 = arcsin (\frac{1}{5}) + 2 πn - 0.4636

Simplificar

θ = arcsin (\frac{1}{5}) + 2 πn - 0.4636

θ = arcsin (\frac{1}{5}) + 2 πn - 0.4636

Resolver

θ + 0.4636 = π - arcsin (\frac{5}{5}) + 2 πn : θ = π - arcsin (\frac{1}{5}) + 2 πn - 0.4636

θ + 0.4636 = π - arcsin (\frac{5}{5}) + 2 πn

Simplificar

π - arcsin (\frac{5}{5}) + 2 πn : π - arcsin (\frac{1}{5}) + 2 πn

π - arcsin (\frac{5}{5}) + 2 πn

\frac{5}{5} = \frac{1}{5}

\frac{5}{5}

Aplicar las leyes de los exponentes:

5 = 5^{\frac{1}{2}}

= \frac{5 ^{\frac{1}{2}}}{5}

Aplicar las leyes de los exponentes:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

\frac{5 ^{\frac{1}{2}}}{5 ^{1}} = \frac{1}{5 ^{1 - \frac{1}{2}}}

= \frac{1}{5 ^{1 - \frac{1}{2}}}

Restar:

1 - \frac{1}{2} = \frac{1}{2}

= \frac{1}{5 ^{\frac{1}{2}}}

Aplicar las leyes de los exponentes:

5^{\frac{1}{2}} = 5

= \frac{1}{5}

= π - arcsin (\frac{1}{5}) + 2 πn

θ + 0.4636 = π - arcsin (\frac{1}{5}) + 2 πn

Mover

0.4636

al lado derecho

θ + 0.4636 = π - arcsin (\frac{1}{5}) + 2 πn

Restar

0.4636

de ambos lados

θ + 0.4636 - 0.4636 = π - arcsin (\frac{1}{5}) + 2 πn - 0.4636

Simplificar

θ = π - arcsin (\frac{1}{5}) + 2 πn - 0.4636

θ = π - arcsin (\frac{1}{5}) + 2 πn - 0.4636

θ = arcsin (\frac{1}{5}) + 2 πn - 0.4636, θ = π - arcsin (\frac{1}{5}) + 2 πn - 0.4636

Mostrar soluciones en forma decimal

θ = 0.46364 \dots + 2 πn - 0.4636, θ = π - 0.46364 \dots + 2 πn - 0.4636

Ejemplos populares

0= 20/3 sin(10t)+5cos(10t)

0 = \frac{20}{3} sin (10 t) + 5 cos (10 t)

solvefor y,arctan(y)=(t^2)/2 resolver para

y, arctan (y) = \frac{t ^{2}}{2}

cos(-x)=0

cos (- x) = 0

2tan^2(x)+1=0

2 tan^{2} (x) + 1 = 0

solvefor y,arctan(y)=(x^3)/3-2x+c resolver para

y, arctan (y) = \frac{x ^{3}}{3} - 2 x + c