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Popular >

6.5*sin(5x)>= 5.6

Solución

6.5 \cdot sin (5 x) \geq 5.6

Solución

\frac{arcsin ( \frac{56}{65} )}{5} + \frac{2 π}{5} n \leq x \leq \frac{π - arcsin ( \frac{56}{65} )}{5} + \frac{2 π}{5} n

Notación de intervalos

[\frac{arcsin ( \frac{56}{65} )}{5} + \frac{2 π}{5} n, \frac{π - arcsin ( \frac{56}{65} )}{5} + \frac{2 π}{5} n]

Notación decimal

0.20765 \dots + \frac{2 π}{5} n \leq x \leq 0.42066 \dots + \frac{2 π}{5} n

Pasos de solución

6.5 sin (5 x) \geq 5.6

Multiplicar ambos lados por

10

6.5 sin (5 x) \geq 5.6

To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere is one digit to the right of the decimal point, therefore multiply by

10

6.5 sin (5 x) \cdot 10 \geq 5.6 \cdot 10

Simplificar

65 sin (5 x) \geq 56

65 sin (5 x) \geq 56

Dividir ambos lados entre

65

65 sin (5 x) \geq 56

Dividir ambos lados entre

65

\frac{65 sin ( 5 x )}{65} \geq \frac{56}{65}

Simplificar

sin (5 x) \geq \frac{56}{65}

sin (5 x) \geq \frac{56}{65}

Para

sin (x) \geq a

, si

- 1 < a < 1

entonces

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

arcsin (\frac{56}{65}) + 2 πn \leq 5 x \leq π - arcsin (\frac{56}{65}) + 2 πn

a \leq u \leq b

entonces

a \leq u and u \leq b

arcsin (\frac{56}{65}) + 2 πn \leq 5 x and 5 x \leq π - arcsin (\frac{56}{65}) + 2 πn

arcsin (\frac{56}{65}) + 2 πn \leq 5 x : x \geq \frac{arcsin ( \frac{56}{65} )}{5} + \frac{2 πn}{5}

arcsin (\frac{56}{65}) + 2 πn \leq 5 x

Intercambiar lados

5 x \geq arcsin (\frac{56}{65}) + 2 πn

Dividir ambos lados entre

5

5 x \geq arcsin (\frac{56}{65}) + 2 πn

Dividir ambos lados entre

5

\frac{5 x}{5} \geq \frac{arcsin ( \frac{56}{65} )}{5} + \frac{2 πn}{5}

Simplificar

x \geq \frac{arcsin ( \frac{56}{65} )}{5} + \frac{2 πn}{5}

x \geq \frac{arcsin ( \frac{56}{65} )}{5} + \frac{2 πn}{5}

5 x \leq π - arcsin (\frac{56}{65}) + 2 πn : x \leq \frac{π - arcsin ( \frac{56}{65} )}{5} + \frac{2 π}{5} n

5 x \leq π - arcsin (\frac{56}{65}) + 2 πn

Dividir ambos lados entre

5

5 x \leq π - arcsin (\frac{56}{65}) + 2 πn

Dividir ambos lados entre

5

\frac{5 x}{5} \leq \frac{π}{5} - \frac{arcsin ( \frac{56}{65} )}{5} + \frac{2 πn}{5}

Simplificar

x \leq \frac{π}{5} - \frac{arcsin ( \frac{56}{65} )}{5} + \frac{2 πn}{5}

Simplificar

\frac{π}{5} - \frac{arcsin ( \frac{56}{65} )}{5} : \frac{π - arcsin ( \frac{56}{65} )}{5}

\frac{π}{5} - \frac{arcsin ( \frac{56}{65} )}{5}

Aplicar la regla

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

= \frac{π - arcsin ( \frac{56}{65} )}{5}

x \leq \frac{π - arcsin ( \frac{56}{65} )}{5} + \frac{2 π}{5} n

x \leq \frac{π - arcsin ( \frac{56}{65} )}{5} + \frac{2 π}{5} n

Combinar los rangos

x \geq \frac{arcsin ( \frac{56}{65} )}{5} + \frac{2 πn}{5} and x \leq \frac{π - arcsin ( \frac{56}{65} )}{5} + \frac{2 π}{5} n

Mezclar intervalos sobrepuestos

\frac{arcsin ( \frac{56}{65} )}{5} + \frac{2 π}{5} n \leq x \leq \frac{π - arcsin ( \frac{56}{65} )}{5} + \frac{2 π}{5} n

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