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2cos(4θ+20)=0.8

Solución

2 cos (4 θ + 20) = 0.8

Solución

θ = - 5 + \frac{πn}{2} + \frac{1.15927 \dots}{4}, θ = \frac{π}{2} + \frac{πn}{2} - \frac{1.15927 \dots}{4} - 5

Grados

θ = - 269.87344 \dots^{\circ} + 9 0^{\circ} n, θ = - 213.08435 \dots^{\circ} + 9 0^{\circ} n

Pasos de solución

2 cos (4 θ + 20) = 0.8

Dividir ambos lados entre

2

2 cos (4 θ + 20) = 0.8

Dividir ambos lados entre

2

\frac{2 cos ( 4 θ + 20 )}{2} = \frac{0.8}{2}

Simplificar

cos (4 θ + 20) = 0.4

cos (4 θ + 20) = 0.4

Aplicar propiedades trigonométricas inversas

cos (4 θ + 20) = 0.4

Soluciones generales para

cos (4 θ + 20) = 0.4

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = 2 π - arccos (a) + 2 πn

4 θ + 20 = arccos (0.4) + 2 πn, 4 θ + 20 = 2 π - arccos (0.4) + 2 πn

4 θ + 20 = arccos (0.4) + 2 πn, 4 θ + 20 = 2 π - arccos (0.4) + 2 πn

Resolver

4 θ + 20 = arccos (0.4) + 2 πn : θ = - 5 + \frac{πn}{2} + \frac{arccos ( 0.4 )}{4}

4 θ + 20 = arccos (0.4) + 2 πn

Mover

20

al lado derecho

4 θ + 20 = arccos (0.4) + 2 πn

Restar

20

de ambos lados

4 θ + 20 - 20 = arccos (0.4) + 2 πn - 20

Simplificar

4 θ = arccos (0.4) + 2 πn - 20

4 θ = arccos (0.4) + 2 πn - 20

Dividir ambos lados entre

4

4 θ = arccos (0.4) + 2 πn - 20

Dividir ambos lados entre

4

\frac{4 θ}{4} = \frac{arccos ( 0.4 )}{4} + \frac{2 πn}{4} - \frac{20}{4}

Simplificar

\frac{4 θ}{4} = \frac{arccos ( 0.4 )}{4} + \frac{2 πn}{4} - \frac{20}{4}

Simplificar

\frac{4 θ}{4} : θ

\frac{4 θ}{4}

Dividir:

\frac{4}{4} = 1

= θ

Simplificar

\frac{arccos ( 0.4 )}{4} + \frac{2 πn}{4} - \frac{20}{4} : - 5 + \frac{πn}{2} + \frac{arccos ( 0.4 )}{4}

\frac{arccos ( 0.4 )}{4} + \frac{2 πn}{4} - \frac{20}{4}

Agrupar términos semejantes

= - \frac{20}{4} + \frac{2 πn}{4} + \frac{arccos ( 0.4 )}{4}

Dividir:

\frac{20}{4} = 5

= - 5 + \frac{2 πn}{4} + \frac{arccos ( 0.4 )}{4}

Cancelar

\frac{2 πn}{4} : \frac{πn}{2}

\frac{2 πn}{4}

Eliminar los terminos comunes:

2

= \frac{πn}{2}

= - 5 + \frac{πn}{2} + \frac{arccos ( 0.4 )}{4}

θ = - 5 + \frac{πn}{2} + \frac{arccos ( 0.4 )}{4}

θ = - 5 + \frac{πn}{2} + \frac{arccos ( 0.4 )}{4}

θ = - 5 + \frac{πn}{2} + \frac{arccos ( 0.4 )}{4}

Resolver

4 θ + 20 = 2 π - arccos (0.4) + 2 πn : θ = \frac{π}{2} + \frac{πn}{2} - \frac{arccos ( 0.4 )}{4} - 5

4 θ + 20 = 2 π - arccos (0.4) + 2 πn

Mover

20

al lado derecho

4 θ + 20 = 2 π - arccos (0.4) + 2 πn

Restar

20

de ambos lados

4 θ + 20 - 20 = 2 π - arccos (0.4) + 2 πn - 20

Simplificar

4 θ = 2 π - arccos (0.4) + 2 πn - 20

4 θ = 2 π - arccos (0.4) + 2 πn - 20

Dividir ambos lados entre

4

4 θ = 2 π - arccos (0.4) + 2 πn - 20

Dividir ambos lados entre

4

\frac{4 θ}{4} = \frac{2 π}{4} - \frac{arccos ( 0.4 )}{4} + \frac{2 πn}{4} - \frac{20}{4}

Simplificar

\frac{4 θ}{4} = \frac{2 π}{4} - \frac{arccos ( 0.4 )}{4} + \frac{2 πn}{4} - \frac{20}{4}

Simplificar

\frac{4 θ}{4} : θ

\frac{4 θ}{4}

Dividir:

\frac{4}{4} = 1

= θ

Simplificar

\frac{2 π}{4} - \frac{arccos ( 0.4 )}{4} + \frac{2 πn}{4} - \frac{20}{4} : \frac{π}{2} + \frac{πn}{2} - \frac{arccos ( 0.4 )}{4} - 5

\frac{2 π}{4} - \frac{arccos ( 0.4 )}{4} + \frac{2 πn}{4} - \frac{20}{4}

Agrupar términos semejantes

= \frac{2 π}{4} - \frac{20}{4} + \frac{2 πn}{4} - \frac{arccos ( 0.4 )}{4}

Cancelar

\frac{2 π}{4} : \frac{π}{2}

\frac{2 π}{4}

Eliminar los terminos comunes:

2

= \frac{π}{2}

= \frac{π}{2} - \frac{20}{4} + \frac{2 πn}{4} - \frac{arccos ( 0.4 )}{4}

Dividir:

\frac{20}{4} = 5

= \frac{π}{2} - 5 + \frac{2 πn}{4} - \frac{arccos ( 0.4 )}{4}

Cancelar

\frac{2 πn}{4} : \frac{πn}{2}

\frac{2 πn}{4}

Eliminar los terminos comunes:

2

= \frac{πn}{2}

= \frac{π}{2} - 5 + \frac{πn}{2} - \frac{arccos ( 0.4 )}{4}

Agrupar términos semejantes

= \frac{π}{2} + \frac{πn}{2} - \frac{arccos ( 0.4 )}{4} - 5

θ = \frac{π}{2} + \frac{πn}{2} - \frac{arccos ( 0.4 )}{4} - 5

θ = \frac{π}{2} + \frac{πn}{2} - \frac{arccos ( 0.4 )}{4} - 5

θ = \frac{π}{2} + \frac{πn}{2} - \frac{arccos ( 0.4 )}{4} - 5

θ = - 5 + \frac{πn}{2} + \frac{arccos ( 0.4 )}{4}, θ = \frac{π}{2} + \frac{πn}{2} - \frac{arccos ( 0.4 )}{4} - 5

Mostrar soluciones en forma decimal

θ = - 5 + \frac{πn}{2} + \frac{1.15927 \dots}{4}, θ = \frac{π}{2} + \frac{πn}{2} - \frac{1.15927 \dots}{4} - 5

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