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Popular >

-4+cos(4θ)=(-8+sqrt(3))/2

Solución

- 4 + cos (4 θ) = \frac{- 8 + 3}{2}

Solución

θ = \frac{π}{24} + \frac{πn}{2}, θ = \frac{π}{2} - \frac{π}{24} + \frac{πn}{2}

Grados

θ = 7. 5^{\circ} + 9 0^{\circ} n, θ = 82. 5^{\circ} + 9 0^{\circ} n

Pasos de solución

- 4 + cos (4 θ) = \frac{- 8 + 3}{2}

Mover

4

al lado derecho

- 4 + cos (4 θ) = \frac{- 8 + 3}{2}

Sumar

4

a ambos lados

- 4 + cos (4 θ) + 4 = \frac{- 8 + 3}{2} + 4

Simplificar

cos (4 θ) = \frac{- 8 + 3}{2} + 4

cos (4 θ) = \frac{- 8 + 3}{2} + 4

Aplicar propiedades trigonométricas inversas

cos (4 θ) = \frac{- 8 + 3}{2} + 4

Soluciones generales para

cos (4 θ) = \frac{- 8 + 3}{2} + 4

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

4 θ = arccos (\frac{- 8 + 3}{2} + 4) + 2 πn, 4 θ = 2 π - arccos (\frac{- 8 + 3}{2} + 4) + 2 πn

4 θ = arccos (\frac{- 8 + 3}{2} + 4) + 2 πn, 4 θ = 2 π - arccos (\frac{- 8 + 3}{2} + 4) + 2 πn

Resolver

4 θ = arccos (\frac{- 8 + 3}{2} + 4) + 2 πn : θ = \frac{π}{24} + \frac{πn}{2}

4 θ = arccos (\frac{- 8 + 3}{2} + 4) + 2 πn

Simplificar

arccos (\frac{- 8 + 3}{2} + 4) + 2 πn : \frac{π}{6} + 2 πn

arccos (\frac{- 8 + 3}{2} + 4) + 2 πn

Utilizar la siguiente identidad trivial:

arccos (\frac{3 - 8}{2} + 4) = \frac{π}{6}

x - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 arccos (x) π \frac{5 π}{6} \frac{3 π}{4} \frac{2 π}{3} \frac{π}{2} \frac{π}{3} \frac{π}{4} \frac{π}{6} 0 arccos (x) 18 0^{\circ} 15 0^{\circ} 13 5^{\circ} 12 0^{\circ} 9 0^{\circ} 6 0^{\circ} 4 5^{\circ} 3 0^{\circ} 0^{\circ}

= \frac{π}{6} + 2 πn

4 θ = \frac{π}{6} + 2 πn

Dividir ambos lados entre

4

4 θ = \frac{π}{6} + 2 πn

Dividir ambos lados entre

4

\frac{4 θ}{4} = \frac{\frac{π}{6}}{4} + \frac{2 πn}{4}

Simplificar

\frac{4 θ}{4} = \frac{\frac{π}{6}}{4} + \frac{2 πn}{4}

Simplificar

\frac{4 θ}{4} : θ

\frac{4 θ}{4}

Dividir:

\frac{4}{4} = 1

= θ

Simplificar

\frac{\frac{π}{6}}{4} + \frac{2 πn}{4} : \frac{π}{24} + \frac{πn}{2}

\frac{\frac{π}{6}}{4} + \frac{2 πn}{4}

\frac{\frac{π}{6}}{4} = \frac{π}{24}

\frac{\frac{π}{6}}{4}

Aplicar las propiedades de las fracciones:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{π}{6 \cdot 4}

Multiplicar los numeros:

6 \cdot 4 = 24

= \frac{π}{24}

\frac{2 πn}{4} = \frac{πn}{2}

\frac{2 πn}{4}

Eliminar los terminos comunes:

2

= \frac{πn}{2}

= \frac{π}{24} + \frac{πn}{2}

θ = \frac{π}{24} + \frac{πn}{2}

θ = \frac{π}{24} + \frac{πn}{2}

θ = \frac{π}{24} + \frac{πn}{2}

Resolver

4 θ = 2 π - arccos (\frac{- 8 + 3}{2} + 4) + 2 πn : θ = \frac{π}{2} - \frac{π}{24} + \frac{πn}{2}

4 θ = 2 π - arccos (\frac{- 8 + 3}{2} + 4) + 2 πn

Simplificar

2 π - arccos (\frac{- 8 + 3}{2} + 4) + 2 πn : 2 π - \frac{π}{6} + 2 πn

2 π - arccos (\frac{- 8 + 3}{2} + 4) + 2 πn

Utilizar la siguiente identidad trivial:

arccos (\frac{3 - 8}{2} + 4) = \frac{π}{6}

x - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 arccos (x) π \frac{5 π}{6} \frac{3 π}{4} \frac{2 π}{3} \frac{π}{2} \frac{π}{3} \frac{π}{4} \frac{π}{6} 0 arccos (x) 18 0^{\circ} 15 0^{\circ} 13 5^{\circ} 12 0^{\circ} 9 0^{\circ} 6 0^{\circ} 4 5^{\circ} 3 0^{\circ} 0^{\circ}

= 2 π - \frac{π}{6} + 2 πn

4 θ = 2 π - \frac{π}{6} + 2 πn

Dividir ambos lados entre

4

4 θ = 2 π - \frac{π}{6} + 2 πn

Dividir ambos lados entre

4

\frac{4 θ}{4} = \frac{2 π}{4} - \frac{\frac{π}{6}}{4} + \frac{2 πn}{4}

Simplificar

\frac{4 θ}{4} = \frac{2 π}{4} - \frac{\frac{π}{6}}{4} + \frac{2 πn}{4}

Simplificar

\frac{4 θ}{4} : θ

\frac{4 θ}{4}

Dividir:

\frac{4}{4} = 1

= θ

Simplificar

\frac{2 π}{4} - \frac{\frac{π}{6}}{4} + \frac{2 πn}{4} : \frac{π}{2} - \frac{π}{24} + \frac{πn}{2}

\frac{2 π}{4} - \frac{\frac{π}{6}}{4} + \frac{2 πn}{4}

\frac{2 π}{4} = \frac{π}{2}

\frac{2 π}{4}

Eliminar los terminos comunes:

2

= \frac{π}{2}

\frac{\frac{π}{6}}{4} = \frac{π}{24}

\frac{\frac{π}{6}}{4}

Aplicar las propiedades de las fracciones:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{π}{6 \cdot 4}

Multiplicar los numeros:

6 \cdot 4 = 24

= \frac{π}{24}

\frac{2 πn}{4} = \frac{πn}{2}

\frac{2 πn}{4}

Eliminar los terminos comunes:

2

= \frac{πn}{2}

= \frac{π}{2} - \frac{π}{24} + \frac{πn}{2}

θ = \frac{π}{2} - \frac{π}{24} + \frac{πn}{2}

θ = \frac{π}{2} - \frac{π}{24} + \frac{πn}{2}

θ = \frac{π}{2} - \frac{π}{24} + \frac{πn}{2}

θ = \frac{π}{24} + \frac{πn}{2}, θ = \frac{π}{2} - \frac{π}{24} + \frac{πn}{2}

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