English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Trigonometría >

50sin(-pi/2 x-pi/2)>=-5

Solución

50 sin (- \frac{π}{2} x - \frac{π}{2}) \geq - 5

Solución

\frac{- 3 π - 2 arcsin ( \frac{1}{10} )}{π} + 4 n \leq x \leq \frac{2 arcsin ( \frac{1}{10} ) - π}{π} + 4 n

Notación de intervalos

[\frac{- 3 π - 2 arcsin ( \frac{1}{10} )}{π} + 4 n, \frac{2 arcsin ( \frac{1}{10} ) - π}{π} + 4 n]

Decimal

- 3.06376 \dots + 4 n \leq x \leq - 0.93623 \dots + 4 n

Pasos de solución

50 sin (- \frac{π}{2} x - \frac{π}{2}) \geq - 5

Dividir ambos lados entre

50

50 sin (- \frac{π}{2} x - \frac{π}{2}) \geq - 5

Dividir ambos lados entre

50

\frac{50 sin ( - \frac{π}{2} x - \frac{π}{2} )}{50} \geq \frac{- 5}{50}

Simplificar

\frac{50 sin ( - \frac{π}{2} x - \frac{π}{2} )}{50} \geq \frac{- 5}{50}

Simplificar

\frac{50 sin ( - \frac{π}{2} x - \frac{π}{2} )}{50} : sin (- \frac{π}{2} x - \frac{π}{2})

\frac{50 sin ( - \frac{π}{2} x - \frac{π}{2} )}{50}

Dividir:

\frac{50}{50} = 1

= sin (- \frac{π}{2} x - \frac{π}{2})

Simplificar

\frac{- 5}{50} : - \frac{1}{10}

\frac{- 5}{50}

Aplicar las propiedades de las fracciones:

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

= - \frac{5}{50}

Eliminar los terminos comunes:

5

= - \frac{1}{10}

sin (- \frac{π}{2} x - \frac{π}{2}) \geq - \frac{1}{10}

sin (- \frac{π}{2} x - \frac{π}{2}) \geq - \frac{1}{10}

sin (- \frac{π}{2} x - \frac{π}{2}) \geq - \frac{1}{10}

Factorizar

- 1

desde

- \frac{π}{2} x - \frac{π}{2} : - (\frac{π}{2} x + \frac{π}{2})

sin (- (\frac{π}{2} x + \frac{π}{2})) \geq - \frac{1}{10}

Usar la siguiente identidad:

sin (- x) = - sin (x)

- sin (\frac{π}{2} + x \frac{π}{2}) \geq - \frac{1}{10}

Multiplicar ambos lados por

- 1

- sin (\frac{π}{2} + x \frac{π}{2}) \geq - \frac{1}{10}

Multiplicar ambos lados por -1 (invierte la desigualdad)

(- sin (\frac{π}{2} + x \frac{π}{2})) (- 1) \leq (- \frac{1}{10}) (- 1)

Simplificar

sin (\frac{π}{2} + x \frac{π}{2}) \leq \frac{1}{10}

sin (\frac{π}{2} + x \frac{π}{2}) \leq \frac{1}{10}

Para

sin (x) \leq a

, si

- 1 < a < 1

entonces

- π - arcsin (a) + 2 πn \leq x \leq arcsin (a) + 2 πn

- π - arcsin (\frac{1}{10}) + 2 πn \leq (\frac{π}{2} + x \frac{π}{2}) \leq arcsin (\frac{1}{10}) + 2 πn

a \leq u \leq b

entonces

a \leq u and u \leq b

- π - arcsin (\frac{1}{10}) + 2 πn \leq \frac{π}{2} + x \frac{π}{2} and \frac{π}{2} + x \frac{π}{2} \leq arcsin (\frac{1}{10}) + 2 πn

- π - arcsin (\frac{1}{10}) + 2 πn \leq \frac{π}{2} + x \frac{π}{2} : x \geq \frac{- 3 π - 2 arcsin ( \frac{1}{10} )}{π} + 4 n

- π - arcsin (\frac{1}{10}) + 2 πn \leq \frac{π}{2} + x \frac{π}{2}

Intercambiar lados

\frac{π}{2} + x \frac{π}{2} \geq - π - arcsin (\frac{1}{10}) + 2 πn

Desplace

\frac{π}{2}

a la derecha

\frac{π}{2} + x \frac{π}{2} \geq - π - arcsin (\frac{1}{10}) + 2 πn

Restar

\frac{π}{2}

de ambos lados

\frac{π}{2} + x \frac{π}{2} - \frac{π}{2} \geq - π - arcsin (\frac{1}{10}) + 2 πn - \frac{π}{2}

Simplificar

x \frac{π}{2} \geq - π - arcsin (\frac{1}{10}) + 2 πn - \frac{π}{2}

x \frac{π}{2} \geq - π - arcsin (\frac{1}{10}) + 2 πn - \frac{π}{2}

Multiplicar ambos lados por

2

x \frac{π}{2} \geq - π - arcsin (\frac{1}{10}) + 2 πn - \frac{π}{2}

Multiplicar ambos lados por

2

2 x \frac{π}{2} \geq - 2 π - 2 arcsin (\frac{1}{10}) + 2 \cdot 2 πn - 2 \cdot \frac{π}{2}

Simplificar

2 x \frac{π}{2} \geq - 2 π - 2 arcsin (\frac{1}{10}) + 2 \cdot 2 πn - 2 \cdot \frac{π}{2}

Simplificar

2 x \frac{π}{2} : π x

2 x \frac{π}{2}

Multiplicar fracciones:

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

= \frac{2 π}{2} x

Eliminar los terminos comunes:

2

= x π

Simplificar

- 2 π - 2 arcsin (\frac{1}{10}) + 2 \cdot 2 πn - 2 \cdot \frac{π}{2} : - 3 π + 4 πn - 2 arcsin (\frac{1}{10})

- 2 π - 2 arcsin (\frac{1}{10}) + 2 \cdot 2 πn - 2 \cdot \frac{π}{2}

2 \cdot 2 πn = 4 πn

2 \cdot 2 πn

Multiplicar los numeros:

2 \cdot 2 = 4

= 4 πn

2 \cdot \frac{π}{2} = π

2 \cdot \frac{π}{2}

Multiplicar fracciones:

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

= \frac{π 2}{2}

Eliminar los terminos comunes:

2

= π

= - 2 π - 2 arcsin (\frac{1}{10}) + 4 πn - π

Agrupar términos semejantes

= - 2 π - π + 4 πn - 2 arcsin (\frac{1}{10})

Sumar elementos similares:

- 2 π - π = - 3 π

= - 3 π + 4 πn - 2 arcsin (\frac{1}{10})

π x \geq - 3 π + 4 πn - 2 arcsin (\frac{1}{10})

π x \geq - 3 π + 4 πn - 2 arcsin (\frac{1}{10})

π x \geq - 3 π + 4 πn - 2 arcsin (\frac{1}{10})

Dividir ambos lados entre

π

π x \geq - 3 π + 4 πn - 2 arcsin (\frac{1}{10})

Dividir ambos lados entre

π

\frac{π x}{π} \geq - \frac{3 π}{π} + \frac{4 πn}{π} - \frac{2 arcsin ( \frac{1}{10} )}{π}

Simplificar

\frac{π x}{π} \geq - \frac{3 π}{π} + \frac{4 πn}{π} - \frac{2 arcsin ( \frac{1}{10} )}{π}

Simplificar

\frac{π x}{π} : x

\frac{π x}{π}

Eliminar los terminos comunes:

π

= x

Simplificar

- \frac{3 π}{π} + \frac{4 πn}{π} - \frac{2 arcsin ( \frac{1}{10} )}{π} : - 3 + 4 n - \frac{2 arcsin ( \frac{1}{10} )}{π}

- \frac{3 π}{π} + \frac{4 πn}{π} - \frac{2 arcsin ( \frac{1}{10} )}{π}

Cancelar

\frac{3 π}{π} : 3

\frac{3 π}{π}

Eliminar los terminos comunes:

π

= 3

= - 3 + \frac{4 πn}{π} - \frac{2 arcsin ( \frac{1}{10} )}{π}

Cancelar

\frac{4 πn}{π} : 4 n

\frac{4 πn}{π}

Eliminar los terminos comunes:

π

= 4 n

= - 3 + 4 n - \frac{2 arcsin ( \frac{1}{10} )}{π}

x \geq - 3 + 4 n - \frac{2 arcsin ( \frac{1}{10} )}{π}

x \geq - 3 + 4 n - \frac{2 arcsin ( \frac{1}{10} )}{π}

Simplificar

- 3 - \frac{2 arcsin ( \frac{1}{10} )}{π} : \frac{- 3 π - 2 arcsin ( \frac{1}{10} )}{π}

- 3 - \frac{2 arcsin ( \frac{1}{10} )}{π}

Convertir a fracción:

3 = \frac{3 π}{π}

= - \frac{3 π}{π} - \frac{2 arcsin ( \frac{1}{10} )}{π}

Ya que los denominadores son iguales, combinar las fracciones:

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

= \frac{- 3 π - 2 arcsin ( \frac{1}{10} )}{π}

x \geq \frac{- 3 π - 2 arcsin ( \frac{1}{10} )}{π} + 4 n

x \geq \frac{- 3 π - 2 arcsin ( \frac{1}{10} )}{π} + 4 n

\frac{π}{2} + x \frac{π}{2} \leq arcsin (\frac{1}{10}) + 2 πn : x \leq \frac{2 arcsin ( \frac{1}{10} ) - π}{π} + 4 n

\frac{π}{2} + x \frac{π}{2} \leq arcsin (\frac{1}{10}) + 2 πn

Desplace

\frac{π}{2}

a la derecha

\frac{π}{2} + x \frac{π}{2} \leq arcsin (\frac{1}{10}) + 2 πn

Restar

\frac{π}{2}

de ambos lados

\frac{π}{2} + x \frac{π}{2} - \frac{π}{2} \leq arcsin (\frac{1}{10}) + 2 πn - \frac{π}{2}

Simplificar

x \frac{π}{2} \leq arcsin (\frac{1}{10}) + 2 πn - \frac{π}{2}

x \frac{π}{2} \leq arcsin (\frac{1}{10}) + 2 πn - \frac{π}{2}

Multiplicar ambos lados por

2

x \frac{π}{2} \leq arcsin (\frac{1}{10}) + 2 πn - \frac{π}{2}

Multiplicar ambos lados por

2

2 x \frac{π}{2} \leq 2 arcsin (\frac{1}{10}) + 2 \cdot 2 πn - 2 \cdot \frac{π}{2}

Simplificar

2 x \frac{π}{2} \leq 2 arcsin (\frac{1}{10}) + 2 \cdot 2 πn - 2 \cdot \frac{π}{2}

Simplificar

2 x \frac{π}{2} : π x

2 x \frac{π}{2}

Multiplicar fracciones:

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

= \frac{2 π}{2} x

Eliminar los terminos comunes:

2

= x π

Simplificar

2 arcsin (\frac{1}{10}) + 2 \cdot 2 πn - 2 \cdot \frac{π}{2} : 2 arcsin (\frac{1}{10}) + 4 πn - π

2 arcsin (\frac{1}{10}) + 2 \cdot 2 πn - 2 \cdot \frac{π}{2}

2 \cdot 2 πn = 4 πn

2 \cdot 2 πn

Multiplicar los numeros:

2 \cdot 2 = 4

= 4 πn

2 \cdot \frac{π}{2} = π

2 \cdot \frac{π}{2}

Multiplicar fracciones:

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

= \frac{π 2}{2}

Eliminar los terminos comunes:

2

= π

= 2 arcsin (\frac{1}{10}) + 4 πn - π

π x \leq 2 arcsin (\frac{1}{10}) + 4 πn - π

π x \leq 2 arcsin (\frac{1}{10}) + 4 πn - π

π x \leq 2 arcsin (\frac{1}{10}) + 4 πn - π

Dividir ambos lados entre

π

π x \leq 2 arcsin (\frac{1}{10}) + 4 πn - π

Dividir ambos lados entre

π

\frac{π x}{π} \leq \frac{2 arcsin ( \frac{1}{10} )}{π} + \frac{4 πn}{π} - \frac{π}{π}

Simplificar

\frac{π x}{π} \leq \frac{2 arcsin ( \frac{1}{10} )}{π} + \frac{4 πn}{π} - \frac{π}{π}

Simplificar

\frac{π x}{π} : x

\frac{π x}{π}

Eliminar los terminos comunes:

π

= x

Simplificar

\frac{2 arcsin ( \frac{1}{10} )}{π} + \frac{4 πn}{π} - \frac{π}{π} : \frac{2 arcsin ( \frac{1}{10} )}{π} + 4 n - 1

\frac{2 arcsin ( \frac{1}{10} )}{π} + \frac{4 πn}{π} - \frac{π}{π}

Aplicar la regla

\frac{a}{a} = 1

\frac{π}{π} = 1

= \frac{2 arcsin ( \frac{1}{10} )}{π} + \frac{4 πn}{π} - 1

Cancelar

\frac{4 πn}{π} : 4 n

\frac{4 πn}{π}

Eliminar los terminos comunes:

π

= 4 n

= \frac{2 arcsin ( \frac{1}{10} )}{π} + 4 n - 1

x \leq \frac{2 arcsin ( \frac{1}{10} )}{π} + 4 n - 1

x \leq \frac{2 arcsin ( \frac{1}{10} )}{π} + 4 n - 1

Simplificar

\frac{2 arcsin ( \frac{1}{10} )}{π} - 1 : \frac{2 arcsin ( \frac{1}{10} ) - π}{π}

\frac{2 arcsin ( \frac{1}{10} )}{π} - 1

Convertir a fracción:

1 = \frac{1 π}{π}

= \frac{2 arcsin ( \frac{1}{10} )}{π} - \frac{1 π}{π}

Ya que los denominadores son iguales, combinar las fracciones:

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

= \frac{2 arcsin ( \frac{1}{10} ) - 1 π}{π}

Multiplicar:

1 π = π

= \frac{2 arcsin ( \frac{1}{10} ) - π}{π}

x \leq \frac{2 arcsin ( \frac{1}{10} ) - π}{π} + 4 n

x \leq \frac{2 arcsin ( \frac{1}{10} ) - π}{π} + 4 n

Combinar los rangos

x \geq \frac{- 3 π - 2 arcsin ( \frac{1}{10} )}{π} + 4 n and x \leq \frac{2 arcsin ( \frac{1}{10} ) - π}{π} + 4 n

Mezclar intervalos sobrepuestos

\frac{- 3 π - 2 arcsin ( \frac{1}{10} )}{π} + 4 n \leq x \leq \frac{2 arcsin ( \frac{1}{10} ) - π}{π} + 4 n

Ejemplos populares

tan^2(x)>3

sqrt(3)-tan(x)>= 0

cos(x)<= 0,-pi<= x<= pi

(cos(x)+1/2)<= 0

tan(x)>= 1,0<= x<= 2pi