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Popular >

cos(4x)=0.8-0.6

Solución

cos (4 x) = 0.8 - 0.6

Solución

x = \frac{1.36943 \dots}{4} + \frac{πn}{2}, x = \frac{π}{2} - \frac{1.36943 \dots}{4} + \frac{πn}{2}

+1

Grados

x = 19.61576 \dots^{\circ} + 9 0^{\circ} n, x = 70.38423 \dots^{\circ} + 9 0^{\circ} n

Pasos de solución

cos (4 x) = 0.8 - 0.6

Restar:

0.8 - 0.6 = 0.2

cos (4 x) = 0.2

Aplicar propiedades trigonométricas inversas

cos (4 x) = 0.2

Soluciones generales para

cos (4 x) = 0.2

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

4 x = arccos (0.2) + 2 πn, 4 x = 2 π - arccos (0.2) + 2 πn

4 x = arccos (0.2) + 2 πn, 4 x = 2 π - arccos (0.2) + 2 πn

Resolver

4 x = arccos (0.2) + 2 πn : x = \frac{arccos ( 0.2 )}{4} + \frac{πn}{2}

4 x = arccos (0.2) + 2 πn

Dividir ambos lados entre

4

4 x = arccos (0.2) + 2 πn

Dividir ambos lados entre

4

\frac{4 x}{4} = \frac{arccos ( 0.2 )}{4} + \frac{2 πn}{4}

Simplificar

x = \frac{arccos ( 0.2 )}{4} + \frac{πn}{2}

x = \frac{arccos ( 0.2 )}{4} + \frac{πn}{2}

Resolver

4 x = 2 π - arccos (0.2) + 2 πn : x = \frac{π}{2} - \frac{arccos ( 0.2 )}{4} + \frac{πn}{2}

4 x = 2 π - arccos (0.2) + 2 πn

Dividir ambos lados entre

4

4 x = 2 π - arccos (0.2) + 2 πn

Dividir ambos lados entre

4

\frac{4 x}{4} = \frac{2 π}{4} - \frac{arccos ( 0.2 )}{4} + \frac{2 πn}{4}

Simplificar

\frac{4 x}{4} = \frac{2 π}{4} - \frac{arccos ( 0.2 )}{4} + \frac{2 πn}{4}

Simplificar

\frac{4 x}{4} : x

\frac{4 x}{4}

Dividir:

\frac{4}{4} = 1

= x

Simplificar

\frac{2 π}{4} - \frac{arccos ( 0.2 )}{4} + \frac{2 πn}{4} : \frac{π}{2} - \frac{arccos ( 0.2 )}{4} + \frac{πn}{2}

\frac{2 π}{4} - \frac{arccos ( 0.2 )}{4} + \frac{2 πn}{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{arccos ( 0.2 )}{4} + \frac{2 πn}{4}

Cancelar

\frac{2 πn}{4} : \frac{πn}{2}

\frac{2 πn}{4}

Eliminar los terminos comunes:

2

= \frac{πn}{2}

= \frac{π}{2} - \frac{arccos ( 0.2 )}{4} + \frac{πn}{2}

x = \frac{π}{2} - \frac{arccos ( 0.2 )}{4} + \frac{πn}{2}

x = \frac{π}{2} - \frac{arccos ( 0.2 )}{4} + \frac{πn}{2}

x = \frac{π}{2} - \frac{arccos ( 0.2 )}{4} + \frac{πn}{2}

x = \frac{arccos ( 0.2 )}{4} + \frac{πn}{2}, x = \frac{π}{2} - \frac{arccos ( 0.2 )}{4} + \frac{πn}{2}

Mostrar soluciones en forma decimal

x = \frac{1.36943 \dots}{4} + \frac{πn}{2}, x = \frac{π}{2} - \frac{1.36943 \dots}{4} + \frac{πn}{2}

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