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tan(x)=(5+cos(x))/(6sin(x)cos(x))

Solución

tan (x) = \frac{5 + cos ( x )}{6 sin ( x ) cos ( x )}

Solución

x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn, x = 1.23095 \dots + 2 πn, x = 2 π - 1.23095 \dots + 2 πn

Grados

x = 12 0^{\circ} + 36 0^{\circ} n, x = 24 0^{\circ} + 36 0^{\circ} n, x = 70.52877 \dots^{\circ} + 36 0^{\circ} n, x = 289.47122 \dots^{\circ} + 36 0^{\circ} n

Pasos de solución

tan (x) = \frac{5 + cos ( x )}{6 sin ( x ) cos ( x )}

Restar

\frac{5 + cos ( x )}{6 sin ( x ) cos ( x )}

de ambos lados

tan (x) - \frac{5 + cos ( x )}{6 sin ( x ) cos ( x )} = 0

Simplificar

tan (x) - \frac{5 + cos ( x )}{6 sin ( x ) cos ( x )} : \frac{6 tan ( x ) sin ( x ) cos ( x ) - 5 - cos ( x )}{6 sin ( x ) cos ( x )}

tan (x) - \frac{5 + cos ( x )}{6 sin ( x ) cos ( x )}

Convertir a fracción:

tan (x) = \frac{tan ( x ) 6 sin ( x ) cos ( x )}{6 sin ( x ) cos ( x )}

= \frac{tan ( x ) \cdot 6 sin ( x ) cos ( x )}{6 sin ( x ) cos ( x )} - \frac{5 + cos ( x )}{6 sin ( x ) cos ( x )}

Ya que los denominadores son iguales, combinar las fracciones:

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

= \frac{tan ( x ) \cdot 6 sin ( x ) cos ( x ) - ( 5 + cos ( x ) )}{6 sin ( x ) cos ( x )}

Expandir

tan (x) \cdot 6 sin (x) cos (x) - (5 + cos (x)) : tan (x) \cdot 6 sin (x) cos (x) - 5 - cos (x)

tan (x) \cdot 6 sin (x) cos (x) - (5 + cos (x))

= 6 tan (x) sin (x) cos (x) - (5 + cos (x))

- (5 + cos (x)) : - 5 - cos (x)

- (5 + cos (x))

Poner los parentesis

= - (5) - (cos (x))

Aplicar las reglas de los signos

+ (- a) = - a

= - 5 - cos (x)

= tan (x) \cdot 6 sin (x) cos (x) - 5 - cos (x)

= \frac{6 tan ( x ) sin ( x ) cos ( x ) - 5 - cos ( x )}{6 sin ( x ) cos ( x )}

\frac{6 tan ( x ) sin ( x ) cos ( x ) - 5 - cos ( x )}{6 sin ( x ) cos ( x )} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

6 tan (x) sin (x) cos (x) - 5 - cos (x) = 0

Expresar con seno, coseno

6 \cdot \frac{sin ( x )}{cos ( x )} sin (x) cos (x) - 5 - cos (x) = 0

Simplificar

6 \cdot \frac{sin ( x )}{cos ( x )} sin (x) cos (x) - 5 - cos (x) : 6 sin^{2} (x) - 5 - cos (x)

6 \cdot \frac{sin ( x )}{cos ( x )} sin (x) cos (x) - 5 - cos (x)

6 \cdot \frac{sin ( x )}{cos ( x )} sin (x) cos (x) = 6 sin^{2} (x)

6 \cdot \frac{sin ( x )}{cos ( x )} sin (x) cos (x)

Multiplicar fracciones:

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

= \frac{sin ( x ) \cdot 6 sin ( x ) cos ( x )}{cos ( x )}

Eliminar los terminos comunes:

cos (x)

= sin (x) \cdot 6 sin (x)

Aplicar las leyes de los exponentes:

a^{b} \cdot a^{c} = a^{b + c}

sin (x) sin (x) = sin^{1 + 1} (x)

= 6 sin^{1 + 1} (x)

Sumar:

1 + 1 = 2

= 6 sin^{2} (x)

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

6 sin^{2} (x) - 5 - cos (x) = 0

Sumar

cos (x)

a ambos lados

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

Elevar al cuadrado ambos lados

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

Restar

cos^{2} (x)

de ambos lados

(6 sin^{2} (x) - 5)^{2} - cos^{2} (x) = 0

Factorizar

(6 sin^{2} (x) - 5)^{2} - cos^{2} (x) : (6 sin^{2} (x) - 5 + cos (x)) (6 sin^{2} (x) - 5 - cos (x))

(6 sin^{2} (x) - 5)^{2} - cos^{2} (x)

Aplicar la siguiente regla para binomios al cuadrado:

x^{2} - y^{2} = (x + y) (x - y)

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

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

Simplificar

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

(6 sin^{2} (x) - 5 + cos (x)) (6 sin^{2} (x) - 5 - cos (x)) = 0

Resolver cada parte por separado

6 sin^{2} (x) - 5 + cos (x) = 0 or 6 sin^{2} (x) - 5 - cos (x) = 0

6 sin^{2} (x) - 5 + cos (x) = 0 : x = arccos (- \frac{1}{3}) + 2 πn, x = - arccos (- \frac{1}{3}) + 2 πn, x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

6 sin^{2} (x) - 5 + cos (x) = 0

Re-escribir usando identidades trigonométricas

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

Utilizar la identidad pitagórica:

cos^{2} (x) + sin^{2} (x) = 1

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

= - 5 + cos (x) + 6 (1 - cos^{2} (x))

Simplificar

- 5 + cos (x) + 6 (1 - cos^{2} (x)) : cos (x) - 6 cos^{2} (x) + 1

- 5 + cos (x) + 6 (1 - cos^{2} (x))

Expandir

6 (1 - cos^{2} (x)) : 6 - 6 cos^{2} (x)

6 (1 - cos^{2} (x))

Poner los parentesis utilizando:

a (b - c) = ab - a c

a = 6, b = 1, c = cos^{2} (x)

= 6 \cdot 1 - 6 cos^{2} (x)

Multiplicar los numeros:

6 \cdot 1 = 6

= 6 - 6 cos^{2} (x)

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

Simplificar

- 5 + cos (x) + 6 - 6 cos^{2} (x) : cos (x) - 6 cos^{2} (x) + 1

- 5 + cos (x) + 6 - 6 cos^{2} (x)

Agrupar términos semejantes

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

Sumar/restar lo siguiente:

- 5 + 6 = 1

= cos (x) - 6 cos^{2} (x) + 1

= cos (x) - 6 cos^{2} (x) + 1

= cos (x) - 6 cos^{2} (x) + 1

1 + cos (x) - 6 cos^{2} (x) = 0

Usando el método de sustitución

1 + cos (x) - 6 cos^{2} (x) = 0

Sea:

cos (x) = u

1 + u - 6 u^{2} = 0

1 + u - 6 u^{2} = 0 : u = - \frac{1}{3}, u = \frac{1}{2}

1 + u - 6 u^{2} = 0

Escribir en la forma binómica

a x^{2} + b x + c = 0

- 6 u^{2} + u + 1 = 0

Resolver con la fórmula general para ecuaciones de segundo grado:

- 6 u^{2} + u + 1 = 0

Formula general para ecuaciones de segundo grado:

Para

a = - 6, b = 1, c = 1

u_{1, 2} = \frac{- 1 \pm 1 ^{2} - 4 ( - 6 ) \cdot 1}{2 ( - 6 )}

u_{1, 2} = \frac{- 1 \pm 1 ^{2} - 4 ( - 6 ) \cdot 1}{2 ( - 6 )}

1^{2} - 4 (- 6) \cdot 1 = 5

1^{2} - 4 (- 6) \cdot 1

Aplicar la regla

1^{a} = 1

1^{2} = 1

= 1 - 4 (- 6) \cdot 1

Aplicar la regla

- (- a) = a

= 1 + 4 \cdot 6 \cdot 1

Multiplicar los numeros:

4 \cdot 6 \cdot 1 = 24

= 1 + 24

Sumar:

1 + 24 = 25

= 25

Descomponer el número en factores primos:

25 = 5^{2}

= 5^{2}

Aplicar las leyes de los exponentes:

5^{2} = 5

= 5

u_{1, 2} = \frac{- 1 \pm 5}{2 ( - 6 )}

Separar las soluciones

u_{1} = \frac{- 1 + 5}{2 ( - 6 )}, u_{2} = \frac{- 1 - 5}{2 ( - 6 )}

u = \frac{- 1 + 5}{2 ( - 6 )} : - \frac{1}{3}

\frac{- 1 + 5}{2 ( - 6 )}

Quitar los parentesis:

(- a) = - a

= \frac{- 1 + 5}{- 2 \cdot 6}

Sumar/restar lo siguiente:

- 1 + 5 = 4

= \frac{4}{- 2 \cdot 6}

Multiplicar los numeros:

2 \cdot 6 = 12

= \frac{4}{- 12}

Aplicar las propiedades de las fracciones:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{4}{12}

Eliminar los terminos comunes:

4

= - \frac{1}{3}

u = \frac{- 1 - 5}{2 ( - 6 )} : \frac{1}{2}

\frac{- 1 - 5}{2 ( - 6 )}

Quitar los parentesis:

(- a) = - a

= \frac{- 1 - 5}{- 2 \cdot 6}

Restar:

- 1 - 5 = - 6

= \frac{- 6}{- 2 \cdot 6}

Multiplicar los numeros:

2 \cdot 6 = 12

= \frac{- 6}{- 12}

Aplicar las propiedades de las fracciones:

\frac{- a}{- b} = \frac{a}{b}

= \frac{6}{12}

Eliminar los terminos comunes:

6

= \frac{1}{2}

Las soluciones a la ecuación de segundo grado son:

u = - \frac{1}{3}, u = \frac{1}{2}

Sustituir en la ecuación

u = cos (x)

cos (x) = - \frac{1}{3}, cos (x) = \frac{1}{2}

cos (x) = - \frac{1}{3}, cos (x) = \frac{1}{2}

cos (x) = - \frac{1}{3} : x = arccos (- \frac{1}{3}) + 2 πn, x = - arccos (- \frac{1}{3}) + 2 πn

cos (x) = - \frac{1}{3}

Aplicar propiedades trigonométricas inversas

cos (x) = - \frac{1}{3}

Soluciones generales para

cos (x) = - \frac{1}{3}

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

x = arccos (- \frac{1}{3}) + 2 πn, x = - arccos (- \frac{1}{3}) + 2 πn

x = arccos (- \frac{1}{3}) + 2 πn, x = - arccos (- \frac{1}{3}) + 2 πn

cos (x) = \frac{1}{2} : x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

cos (x) = \frac{1}{2}

Soluciones generales para

cos (x) = \frac{1}{2}

cos (x)

tabla de valores periódicos con

2 πn

intervalos:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Combinar toda las soluciones

x = arccos (- \frac{1}{3}) + 2 πn, x = - arccos (- \frac{1}{3}) + 2 πn, x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

6 sin^{2} (x) - 5 - cos (x) = 0 : x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn, x = arccos (\frac{1}{3}) + 2 πn, x = 2 π - arccos (\frac{1}{3}) + 2 πn

6 sin^{2} (x) - 5 - cos (x) = 0

Re-escribir usando identidades trigonométricas

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

Utilizar la identidad pitagórica:

cos^{2} (x) + sin^{2} (x) = 1

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

= - 5 - cos (x) + 6 (1 - cos^{2} (x))

Simplificar

- 5 - cos (x) + 6 (1 - cos^{2} (x)) : - 6 cos^{2} (x) - cos (x) + 1

- 5 - cos (x) + 6 (1 - cos^{2} (x))

Expandir

6 (1 - cos^{2} (x)) : 6 - 6 cos^{2} (x)

6 (1 - cos^{2} (x))

Poner los parentesis utilizando:

a (b - c) = ab - a c

a = 6, b = 1, c = cos^{2} (x)

= 6 \cdot 1 - 6 cos^{2} (x)

Multiplicar los numeros:

6 \cdot 1 = 6

= 6 - 6 cos^{2} (x)

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

Simplificar

- 5 - cos (x) + 6 - 6 cos^{2} (x) : - 6 cos^{2} (x) - cos (x) + 1

- 5 - cos (x) + 6 - 6 cos^{2} (x)

Agrupar términos semejantes

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

Sumar/restar lo siguiente:

- 5 + 6 = 1

= - 6 cos^{2} (x) - cos (x) + 1

= - 6 cos^{2} (x) - cos (x) + 1

= - 6 cos^{2} (x) - cos (x) + 1

1 - cos (x) - 6 cos^{2} (x) = 0

Usando el método de sustitución

1 - cos (x) - 6 cos^{2} (x) = 0

Sea:

cos (x) = u

1 - u - 6 u^{2} = 0

1 - u - 6 u^{2} = 0 : u = - \frac{1}{2}, u = \frac{1}{3}

1 - u - 6 u^{2} = 0

Escribir en la forma binómica

a x^{2} + b x + c = 0

- 6 u^{2} - u + 1 = 0

Resolver con la fórmula general para ecuaciones de segundo grado:

- 6 u^{2} - u + 1 = 0

Formula general para ecuaciones de segundo grado:

Para

a = - 6, b = - 1, c = 1

u_{1, 2} = \frac{- ( - 1 ) \pm ( - 1 ) ^{2} - 4 ( - 6 ) \cdot 1}{2 ( - 6 )}

u_{1, 2} = \frac{- ( - 1 ) \pm ( - 1 ) ^{2} - 4 ( - 6 ) \cdot 1}{2 ( - 6 )}

(- 1)^{2} - 4 (- 6) \cdot 1 = 5

(- 1)^{2} - 4 (- 6) \cdot 1

Aplicar la regla

- (- a) = a

= (- 1)^{2} + 4 \cdot 6 \cdot 1

(- 1)^{2} = 1

(- 1)^{2}

Aplicar las leyes de los exponentes:

(- a)^{n} = a^{n},

n

es par

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

= 1^{2}

Aplicar la regla

1^{a} = 1

= 1

4 \cdot 6 \cdot 1 = 24

4 \cdot 6 \cdot 1

Multiplicar los numeros:

4 \cdot 6 \cdot 1 = 24

= 24

= 1 + 24

Sumar:

1 + 24 = 25

= 25

Descomponer el número en factores primos:

25 = 5^{2}

= 5^{2}

Aplicar las leyes de los exponentes:

5^{2} = 5

= 5

u_{1, 2} = \frac{- ( - 1 ) \pm 5}{2 ( - 6 )}

Separar las soluciones

u_{1} = \frac{- ( - 1 ) + 5}{2 ( - 6 )}, u_{2} = \frac{- ( - 1 ) - 5}{2 ( - 6 )}

u = \frac{- ( - 1 ) + 5}{2 ( - 6 )} : - \frac{1}{2}

\frac{- ( - 1 ) + 5}{2 ( - 6 )}

Quitar los parentesis:

(- a) = - a, - (- a) = a

= \frac{1 + 5}{- 2 \cdot 6}

Sumar:

1 + 5 = 6

= \frac{6}{- 2 \cdot 6}

Multiplicar los numeros:

2 \cdot 6 = 12

= \frac{6}{- 12}

Aplicar las propiedades de las fracciones:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{6}{12}

Eliminar los terminos comunes:

6

= - \frac{1}{2}

u = \frac{- ( - 1 ) - 5}{2 ( - 6 )} : \frac{1}{3}

\frac{- ( - 1 ) - 5}{2 ( - 6 )}

Quitar los parentesis:

(- a) = - a, - (- a) = a

= \frac{1 - 5}{- 2 \cdot 6}

Restar:

1 - 5 = - 4

= \frac{- 4}{- 2 \cdot 6}

Multiplicar los numeros:

2 \cdot 6 = 12

= \frac{- 4}{- 12}

Aplicar las propiedades de las fracciones:

\frac{- a}{- b} = \frac{a}{b}

= \frac{4}{12}

Eliminar los terminos comunes:

4

= \frac{1}{3}

Las soluciones a la ecuación de segundo grado son:

u = - \frac{1}{2}, u = \frac{1}{3}

Sustituir en la ecuación

u = cos (x)

cos (x) = - \frac{1}{2}, cos (x) = \frac{1}{3}

cos (x) = - \frac{1}{2}, cos (x) = \frac{1}{3}

cos (x) = - \frac{1}{2} : x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

cos (x) = - \frac{1}{2}

Soluciones generales para

cos (x) = - \frac{1}{2}

cos (x)

tabla de valores periódicos con

2 πn

intervalos:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

cos (x) = \frac{1}{3} : x = arccos (\frac{1}{3}) + 2 πn, x = 2 π - arccos (\frac{1}{3}) + 2 πn

cos (x) = \frac{1}{3}

Aplicar propiedades trigonométricas inversas

cos (x) = \frac{1}{3}

Soluciones generales para

cos (x) = \frac{1}{3}

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

x = arccos (\frac{1}{3}) + 2 πn, x = 2 π - arccos (\frac{1}{3}) + 2 πn

x = arccos (\frac{1}{3}) + 2 πn, x = 2 π - arccos (\frac{1}{3}) + 2 πn

Combinar toda las soluciones

x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn, x = arccos (\frac{1}{3}) + 2 πn, x = 2 π - arccos (\frac{1}{3}) + 2 πn

Combinar toda las soluciones

x = arccos (- \frac{1}{3}) + 2 πn, x = - arccos (- \frac{1}{3}) + 2 πn, x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn, x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn, x = arccos (\frac{1}{3}) + 2 πn, x = 2 π - arccos (\frac{1}{3}) + 2 πn

Verificar las soluciones sustituyendo en la ecuación original

Verificar las soluciones sustituyéndolas en

tan (x) = \frac{5 + cos ( x )}{6 sin ( x ) cos ( x )}

Quitar las que no concuerden con la ecuación.

Verificar la solución

arccos (- \frac{1}{3}) + 2 πn :

Falso

arccos (- \frac{1}{3}) + 2 πn

Sustituir

n = 1

arccos (- \frac{1}{3}) + 2 π 1

Multiplicar

tan (x) = \frac{5 + cos ( x )}{6 sin ( x ) cos ( x )}

por

x = arccos (- \frac{1}{3}) + 2 π 1

tan (arccos (- \frac{1}{3}) + 2 π 1) = \frac{5 + cos ( arccos ( - \frac{1}{3} ) + 2 π 1 )}{6 sin ( arccos ( - \frac{1}{3} ) + 2 π 1 ) cos ( arccos ( - \frac{1}{3} ) + 2 π 1 )}

Simplificar

- 2.82842 \dots = - 2.47487 \dots

\Rightarrow Falso

Verificar la solución

- arccos (- \frac{1}{3}) + 2 πn :

Falso

- arccos (- \frac{1}{3}) + 2 πn

Sustituir

n = 1

- arccos (- \frac{1}{3}) + 2 π 1

Multiplicar

tan (x) = \frac{5 + cos ( x )}{6 sin ( x ) cos ( x )}

por

x = - arccos (- \frac{1}{3}) + 2 π 1

tan (- arccos (- \frac{1}{3}) + 2 π 1) = \frac{5 + cos ( - arccos ( - \frac{1}{3} ) + 2 π 1 )}{6 sin ( - arccos ( - \frac{1}{3} ) + 2 π 1 ) cos ( - arccos ( - \frac{1}{3} ) + 2 π 1 )}

Simplificar

2.82842 \dots = 2.47487 \dots

\Rightarrow Falso

Verificar la solución

\frac{π}{3} + 2 πn :

Falso

\frac{π}{3} + 2 πn

Sustituir

n = 1

\frac{π}{3} + 2 π 1

Multiplicar

tan (x) = \frac{5 + cos ( x )}{6 sin ( x ) cos ( x )}

por

x = \frac{π}{3} + 2 π 1

tan (\frac{π}{3} + 2 π 1) = \frac{5 + cos ( \frac{π}{3} + 2 π 1 )}{6 sin ( \frac{π}{3} + 2 π 1 ) cos ( \frac{π}{3} + 2 π 1 )}

Simplificar

1.73205 \dots = 2.11695 \dots

\Rightarrow Falso

Verificar la solución

\frac{5 π}{3} + 2 πn :

Falso

\frac{5 π}{3} + 2 πn

Sustituir

n = 1

\frac{5 π}{3} + 2 π 1

Multiplicar

tan (x) = \frac{5 + cos ( x )}{6 sin ( x ) cos ( x )}

por

x = \frac{5 π}{3} + 2 π 1

tan (\frac{5 π}{3} + 2 π 1) = \frac{5 + cos ( \frac{5 π}{3} + 2 π 1 )}{6 sin ( \frac{5 π}{3} + 2 π 1 ) cos ( \frac{5 π}{3} + 2 π 1 )}

Simplificar

- 1.73205 \dots = - 2.11695 \dots

\Rightarrow Falso

Verificar la solución

\frac{2 π}{3} + 2 πn :

Verdadero

\frac{2 π}{3} + 2 πn

Sustituir

n = 1

\frac{2 π}{3} + 2 π 1

Multiplicar

tan (x) = \frac{5 + cos ( x )}{6 sin ( x ) cos ( x )}

por

x = \frac{2 π}{3} + 2 π 1

tan (\frac{2 π}{3} + 2 π 1) = \frac{5 + cos ( \frac{2 π}{3} + 2 π 1 )}{6 sin ( \frac{2 π}{3} + 2 π 1 ) cos ( \frac{2 π}{3} + 2 π 1 )}

Simplificar

- 1.73205 \dots = - 1.73205 \dots

\Rightarrow Verdadero

Verificar la solución

\frac{4 π}{3} + 2 πn :

Verdadero

\frac{4 π}{3} + 2 πn

Sustituir

n = 1

\frac{4 π}{3} + 2 π 1

Multiplicar

tan (x) = \frac{5 + cos ( x )}{6 sin ( x ) cos ( x )}

por

x = \frac{4 π}{3} + 2 π 1

tan (\frac{4 π}{3} + 2 π 1) = \frac{5 + cos ( \frac{4 π}{3} + 2 π 1 )}{6 sin ( \frac{4 π}{3} + 2 π 1 ) cos ( \frac{4 π}{3} + 2 π 1 )}

Simplificar

1.73205 \dots = 1.73205 \dots

\Rightarrow Verdadero

Verificar la solución

arccos (\frac{1}{3}) + 2 πn :

Verdadero

arccos (\frac{1}{3}) + 2 πn

Sustituir

n = 1

arccos (\frac{1}{3}) + 2 π 1

Multiplicar

tan (x) = \frac{5 + cos ( x )}{6 sin ( x ) cos ( x )}

por

x = arccos (\frac{1}{3}) + 2 π 1

tan (arccos (\frac{1}{3}) + 2 π 1) = \frac{5 + cos ( arccos ( \frac{1}{3} ) + 2 π 1 )}{6 sin ( arccos ( \frac{1}{3} ) + 2 π 1 ) cos ( arccos ( \frac{1}{3} ) + 2 π 1 )}

Simplificar

2.82842 \dots = 2.82842 \dots

\Rightarrow Verdadero

Verificar la solución

2 π - arccos (\frac{1}{3}) + 2 πn :

Verdadero

2 π - arccos (\frac{1}{3}) + 2 πn

Sustituir

n = 1

2 π - arccos (\frac{1}{3}) + 2 π 1

Multiplicar

tan (x) = \frac{5 + cos ( x )}{6 sin ( x ) cos ( x )}

por

x = 2 π - arccos (\frac{1}{3}) + 2 π 1

tan (2 π - arccos (\frac{1}{3}) + 2 π 1) = \frac{5 + cos ( 2 π - arccos ( \frac{1}{3} ) + 2 π 1 )}{6 sin ( 2 π - arccos ( \frac{1}{3} ) + 2 π 1 ) cos ( 2 π - arccos ( \frac{1}{3} ) + 2 π 1 )}

Simplificar

- 2.82842 \dots = - 2.82842 \dots

\Rightarrow Verdadero

x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn, x = arccos (\frac{1}{3}) + 2 πn, x = 2 π - arccos (\frac{1}{3}) + 2 πn

Mostrar soluciones en forma decimal

x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn, x = 1.23095 \dots + 2 πn, x = 2 π - 1.23095 \dots + 2 πn

Ejemplos populares

cos(x-1)= 1/2 ,0<= x<= 360

cos (x - 1) = \frac{1}{2}, 0^{\circ} \leq x \leq 36 0^{\circ}

cos(t)= 21/29

cos (t) = \frac{21}{29}

cos(x)=sin(x-pi/3)

cos (x) = sin (x - \frac{π}{3})

sin(x+pi/4)+sin(x+pi/4)=-1

sin (x + \frac{π}{4}) + sin (x + \frac{π}{4}) = - 1

cos(x)-sin^2(x)=0

cos (x) - sin^{2} (x) = 0