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2cos^2(2x)+9cos(4x)=-2.4214900000000…

Solución

2 \cdot cos^{2} (2 x) + 9 \cdot cos (4 x) = - 2.4214900000000 \dots

Solución

x = \frac{0.95999 \dots}{2} + πn, x = π - \frac{0.95999 \dots}{2} + πn, x = \frac{2.18159 \dots}{2} + πn, x = - \frac{2.18159 \dots}{2} + πn

Grados

x = 27.50196 \dots^{\circ} + 18 0^{\circ} n, x = 152.49803 \dots^{\circ} + 18 0^{\circ} n, x = 62.49803 \dots^{\circ} + 18 0^{\circ} n, x = - 62.49803 \dots^{\circ} + 18 0^{\circ} n

Pasos de solución

2 cos^{2} (2 x) + 9 cos (4 x) = - 2.42149 \dots

Restar

- 2.42149 \dots

de ambos lados

2 cos^{2} (2 x) + 9 cos (4 x) + 2.42149 \dots = 0

Re-escribir usando identidades trigonométricas

2.42149 \dots + 2 cos^{2} (2 x) + 9 cos (4 x)

cos (4 x) = 2 cos^{2} (2 x) - 1

cos (4 x)

Reescribir como

= cos (2 \cdot 2 x)

Utilizar la identidad trigonométrica del ángulo doble:

cos (2 x) = 2 cos^{2} (x) - 1

cos (2 \cdot 2 x) = 2 cos^{2} (2 x) - 1

= 2 cos^{2} (2 x) - 1

= 2.42149 \dots + 2 cos^{2} (2 x) + 9 (2 cos^{2} (2 x) - 1)

Simplificar

2.42149 \dots + 2 cos^{2} (2 x) + 9 (2 cos^{2} (2 x) - 1) : 20 cos^{2} (2 x) - 6.57851

2.42149 \dots + 2 cos^{2} (2 x) + 9 (2 cos^{2} (2 x) - 1)

Expandir

9 (2 cos^{2} (2 x) - 1) : 18 cos^{2} (2 x) - 9

9 (2 cos^{2} (2 x) - 1)

Poner los parentesis utilizando:

a (b - c) = ab - a c

a = 9, b = 2 cos^{2} (2 x), c = 1

= 9 \cdot 2 cos^{2} (2 x) - 9 \cdot 1

Simplificar

9 \cdot 2 cos^{2} (2 x) - 9 \cdot 1 : 18 cos^{2} (2 x) - 9

9 \cdot 2 cos^{2} (2 x) - 9 \cdot 1

Multiplicar los numeros:

9 \cdot 2 = 18

= 18 cos^{2} (2 x) - 9 \cdot 1

Multiplicar los numeros:

9 \cdot 1 = 9

= 18 cos^{2} (2 x) - 9

= 18 cos^{2} (2 x) - 9

= 2.42149 \dots + 2 cos^{2} (2 x) + 18 cos^{2} (2 x) - 9

Simplificar

2.42149 \dots + 2 cos^{2} (2 x) + 18 cos^{2} (2 x) - 9 : 20 cos^{2} (2 x) - 6.57851

2.42149 \dots + 2 cos^{2} (2 x) + 18 cos^{2} (2 x) - 9

Sumar elementos similares:

2 cos^{2} (2 x) + 18 cos^{2} (2 x) = 20 cos^{2} (2 x)

= 2.42149 \dots + 20 cos^{2} (2 x) - 9

Agrupar términos semejantes

= 20 cos^{2} (2 x) + 2.42149 \dots - 9

Sumar/restar lo siguiente:

2.42149 \dots - 9 = - 6.57851

= 20 cos^{2} (2 x) - 6.57851

= 20 cos^{2} (2 x) - 6.57851

= 20 cos^{2} (2 x) - 6.57851

- 6.57851 + 20 cos^{2} (2 x) = 0

Usando el método de sustitución

- 6.57851 + 20 cos^{2} (2 x) = 0

Sea:

cos (2 x) = u

- 6.57851 + 20 u^{2} = 0

- 6.57851 + 20 u^{2} = 0 : u = \frac{32.89255}{10}, u = - \frac{32.89255}{10}

- 6.57851 + 20 u^{2} = 0

Mover

6.57851

al lado derecho

- 6.57851 + 20 u^{2} = 0

Sumar

6.57851

a ambos lados

- 6.57851 + 20 u^{2} + 6.57851 = 0 + 6.57851

Simplificar

20 u^{2} = 6.57851

20 u^{2} = 6.57851

Dividir ambos lados entre

20

20 u^{2} = 6.57851

Dividir ambos lados entre

20

\frac{20 u ^{2}}{20} = \frac{6.57851}{20}

Simplificar

u^{2} = \frac{6.57851}{20}

u^{2} = \frac{6.57851}{20}

Para

x^{2} = f (a)

las soluciones son

x = f (a), - f (a)

u = \frac{6.57851}{20}, u = - \frac{6.57851}{20}

\frac{6.57851}{20} = \frac{32.89255}{10}

\frac{6.57851}{20}

Aplicar la siguiente propiedad de los radicales:

asumiendo que

a \geq 0, b \geq 0

= \frac{6.57851}{20}

20 = 25

20

Descomposición en factores primos de

20 : 2^{2} \cdot 5

20

20

divida por

220 = 10 \cdot 2

= 2 \cdot 10

10

divida por

210 = 5 \cdot 2

= 2 \cdot 2 \cdot 5

2, 5

son números primos, por lo tanto, no se pueden factorizar mas

= 2 \cdot 2 \cdot 5

= 2^{2} \cdot 5

= 2^{2} \cdot 5

Aplicar las leyes de los exponentes:

= 5 2^{2}

Aplicar las leyes de los exponentes:

2^{2} = 2

= 25

= \frac{6.57851}{2 5}

Racionalizar

\frac{6.57851}{2 5} : \frac{32.89255}{10}

\frac{6.57851}{2 5}

Multiplicar por el conjugado

\frac{5}{5}

= \frac{6.57851 5}{2 5 5}

6.57851 5 = 32.89255

6.57851 5

Aplicar las leyes de los exponentes:

a b = a \cdot b

5 6.57851 = 5 \cdot 6.57851

= 5 \cdot 6.57851

Multiplicar los numeros:

6.57851 \cdot 5 = 32.89255

= 32.89255

255 = 10

255

Aplicar las leyes de los exponentes:

a a = a

55 = 5

= 2 \cdot 5

Multiplicar los numeros:

2 \cdot 5 = 10

= 10

= \frac{32.89255}{10}

= \frac{32.89255}{10}

- \frac{6.57851}{20} = - \frac{32.89255}{10}

- \frac{6.57851}{20}

Simplificar

\frac{6.57851}{20} : \frac{6.57851}{2 5}

\frac{6.57851}{20}

Aplicar la siguiente propiedad de los radicales:

asumiendo que

a \geq 0, b \geq 0

= \frac{6.57851}{20}

20 = 25

20

Descomposición en factores primos de

20 : 2^{2} \cdot 5

20

20

divida por

220 = 10 \cdot 2

= 2 \cdot 10

10

divida por

210 = 5 \cdot 2

= 2 \cdot 2 \cdot 5

2, 5

son números primos, por lo tanto, no se pueden factorizar mas

= 2 \cdot 2 \cdot 5

= 2^{2} \cdot 5

= 2^{2} \cdot 5

Aplicar las leyes de los exponentes:

= 5 2^{2}

Aplicar las leyes de los exponentes:

2^{2} = 2

= 25

= \frac{6.57851}{2 5}

= - \frac{6.57851}{2 5}

Racionalizar

- \frac{6.57851}{2 5} : - \frac{32.89255}{10}

- \frac{6.57851}{2 5}

Multiplicar por el conjugado

\frac{5}{5}

= - \frac{6.57851 5}{2 5 5}

6.57851 5 = 32.89255

6.57851 5

Aplicar las leyes de los exponentes:

a b = a \cdot b

5 6.57851 = 5 \cdot 6.57851

= 5 \cdot 6.57851

Multiplicar los numeros:

6.57851 \cdot 5 = 32.89255

= 32.89255

255 = 10

255

Aplicar las leyes de los exponentes:

a a = a

55 = 5

= 2 \cdot 5

Multiplicar los numeros:

2 \cdot 5 = 10

= 10

= - \frac{32.89255}{10}

= - \frac{32.89255}{10}

u = \frac{32.89255}{10}, u = - \frac{32.89255}{10}

Sustituir en la ecuación

u = cos (2 x)

cos (2 x) = \frac{32.89255}{10}, cos (2 x) = - \frac{32.89255}{10}

cos (2 x) = \frac{32.89255}{10}, cos (2 x) = - \frac{32.89255}{10}

cos (2 x) = \frac{32.89255}{10} : x = \frac{arccos ( \frac{32.89255}{10} )}{2} + πn, x = π - \frac{arccos ( \frac{32.89255}{10} )}{2} + πn

cos (2 x) = \frac{32.89255}{10}

Aplicar propiedades trigonométricas inversas

cos (2 x) = \frac{32.89255}{10}

Soluciones generales para

cos (2 x) = \frac{32.89255}{10}

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

2 x = arccos (\frac{32.89255}{10}) + 2 πn, 2 x = 2 π - arccos (\frac{32.89255}{10}) + 2 πn

2 x = arccos (\frac{32.89255}{10}) + 2 πn, 2 x = 2 π - arccos (\frac{32.89255}{10}) + 2 πn

Resolver

2 x = arccos (\frac{32.89255}{10}) + 2 πn : x = \frac{arccos ( \frac{32.89255}{10} )}{2} + πn

2 x = arccos (\frac{32.89255}{10}) + 2 πn

Dividir ambos lados entre

2

2 x = arccos (\frac{32.89255}{10}) + 2 πn

Dividir ambos lados entre

2

\frac{2 x}{2} = \frac{arccos ( \frac{32.89255}{10} )}{2} + \frac{2 πn}{2}

Simplificar

x = \frac{arccos ( \frac{32.89255}{10} )}{2} + πn

x = \frac{arccos ( \frac{32.89255}{10} )}{2} + πn

Resolver

2 x = 2 π - arccos (\frac{32.89255}{10}) + 2 πn : x = π - \frac{arccos ( \frac{32.89255}{10} )}{2} + πn

2 x = 2 π - arccos (\frac{32.89255}{10}) + 2 πn

Dividir ambos lados entre

2

2 x = 2 π - arccos (\frac{32.89255}{10}) + 2 πn

Dividir ambos lados entre

2

\frac{2 x}{2} = \frac{2 π}{2} - \frac{arccos ( \frac{32.89255}{10} )}{2} + \frac{2 πn}{2}

Simplificar

x = π - \frac{arccos ( \frac{32.89255}{10} )}{2} + πn

x = π - \frac{arccos ( \frac{32.89255}{10} )}{2} + πn

x = \frac{arccos ( \frac{32.89255}{10} )}{2} + πn, x = π - \frac{arccos ( \frac{32.89255}{10} )}{2} + πn

cos (2 x) = - \frac{32.89255}{10} : x = \frac{arccos ( - \frac{32.89255}{10} )}{2} + πn, x = - \frac{arccos ( - \frac{32.89255}{10} )}{2} + πn

cos (2 x) = - \frac{32.89255}{10}

Aplicar propiedades trigonométricas inversas

cos (2 x) = - \frac{32.89255}{10}

Soluciones generales para

cos (2 x) = - \frac{32.89255}{10}

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

2 x = arccos (- \frac{32.89255}{10}) + 2 πn, 2 x = - arccos (- \frac{32.89255}{10}) + 2 πn

2 x = arccos (- \frac{32.89255}{10}) + 2 πn, 2 x = - arccos (- \frac{32.89255}{10}) + 2 πn

Resolver

2 x = arccos (- \frac{32.89255}{10}) + 2 πn : x = \frac{arccos ( - \frac{32.89255}{10} )}{2} + πn

2 x = arccos (- \frac{32.89255}{10}) + 2 πn

Dividir ambos lados entre

2

2 x = arccos (- \frac{32.89255}{10}) + 2 πn

Dividir ambos lados entre

2

\frac{2 x}{2} = \frac{arccos ( - \frac{32.89255}{10} )}{2} + \frac{2 πn}{2}

Simplificar

x = \frac{arccos ( - \frac{32.89255}{10} )}{2} + πn

x = \frac{arccos ( - \frac{32.89255}{10} )}{2} + πn

Resolver

2 x = - arccos (- \frac{32.89255}{10}) + 2 πn : x = - \frac{arccos ( - \frac{32.89255}{10} )}{2} + πn

2 x = - arccos (- \frac{32.89255}{10}) + 2 πn

Dividir ambos lados entre

2

2 x = - arccos (- \frac{32.89255}{10}) + 2 πn

Dividir ambos lados entre

2

\frac{2 x}{2} = - \frac{arccos ( - \frac{32.89255}{10} )}{2} + \frac{2 πn}{2}

Simplificar

x = - \frac{arccos ( - \frac{32.89255}{10} )}{2} + πn

x = - \frac{arccos ( - \frac{32.89255}{10} )}{2} + πn

x = \frac{arccos ( - \frac{32.89255}{10} )}{2} + πn, x = - \frac{arccos ( - \frac{32.89255}{10} )}{2} + πn

Combinar toda las soluciones

x = \frac{arccos ( \frac{32.89255}{10} )}{2} + πn, x = π - \frac{arccos ( \frac{32.89255}{10} )}{2} + πn, x = \frac{arccos ( - \frac{32.89255}{10} )}{2} + πn, x = - \frac{arccos ( - \frac{32.89255}{10} )}{2} + πn

Mostrar soluciones en forma decimal

x = \frac{0.95999 \dots}{2} + πn, x = π - \frac{0.95999 \dots}{2} + πn, x = \frac{2.18159 \dots}{2} + πn, x = - \frac{2.18159 \dots}{2} + πn

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tan (- x) = tan (x)

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6 sin (θ) = 6 sin (2 θ)

2sin(15)cos(15)=tan(x)

2 sin (1 5^{\circ}) cos (1 5^{\circ}) = tan (x)

6sin^2(x)+5cos(x)=7

6 sin^{2} (x) + 5 cos (x) = 7

sqrt(3)cos(x)+sin(x)=-1

3 cos (x) + sin (x) = - 1

2*cos^2(2x)+9*cos(4x)=-2.4214900000000…

Solución

Solución

Ejemplos populares

2cos^2(2x)+9cos(4x)=-2.4214900000000…