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Popular Trigonometría >

sin(4x+17)>0

Solución

sin (4 x + 1 7^{\circ}) > 0

Solución

- \frac{1 7 ^{\circ}}{4} + \frac{π}{2} n < x < \frac{π - 1 7 ^{\circ}}{4} + \frac{π}{2} n

Notación de intervalos

(- \frac{1 7 ^{\circ}}{4} + \frac{π}{2} n, \frac{π - 1 7 ^{\circ}}{4} + \frac{π}{2} n)

Decimal

- 0.07417 \dots + \frac{π}{2} n < x < 0.71122 \dots + \frac{π}{2} n

Pasos de solución

sin (4 x + 1 7^{\circ}) > 0

Para

sin (x) > a

, si

- 1 \leq a < 1

entonces

arcsin (a) + 2 πn < x < π - arcsin (a) + 2 πn

arcsin (0) + 2 πn < (4 x + 1 7^{\circ}) < π - arcsin (0) + 2 πn

a < u < b

entonces

a < u and u < b

arcsin (0) + 2 πn < 4 x + 1 7^{\circ} and 4 x + 1 7^{\circ} < π - arcsin (0) + 2 πn

arcsin (0) + 2 πn < 4 x + 1 7^{\circ} : x > \frac{πn}{2} - \frac{1 7 ^{\circ}}{4}

arcsin (0) + 2 πn < 4 x + 1 7^{\circ}

Intercambiar lados

4 x + 1 7^{\circ} > arcsin (0) + 2 πn

Simplificar

arcsin (0) + 2 πn : 2 πn

arcsin (0) + 2 πn

Utilizar la siguiente identidad trivial:

arcsin (0) = 0

x 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 arcsin (x) 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} arcsin (x) 0^{\circ} 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ}

= 0 + 2 πn

0 + 2 πn = 2 πn

= 2 πn

4 x + 1 7^{\circ} > 2 πn

Desplace

1 7^{\circ}

a la derecha

4 x + 1 7^{\circ} > 2 πn

Restar

1 7^{\circ}

de ambos lados

4 x + 1 7^{\circ} - 1 7^{\circ} > 2 πn - 1 7^{\circ}

Simplificar

4 x > 2 πn - 1 7^{\circ}

4 x > 2 πn - 1 7^{\circ}

Dividir ambos lados entre

4

4 x > 2 πn - 1 7^{\circ}

Dividir ambos lados entre

4

\frac{4 x}{4} > \frac{2 πn}{4} - \frac{1 7 ^{\circ}}{4}

Simplificar

x > \frac{πn}{2} - \frac{1 7 ^{\circ}}{4}

x > \frac{πn}{2} - \frac{1 7 ^{\circ}}{4}

4 x + 1 7^{\circ} < π - arcsin (0) + 2 πn : x < \frac{π - 1 7 ^{\circ}}{4} + \frac{π}{2} n

4 x + 1 7^{\circ} < π - arcsin (0) + 2 πn

Simplificar

π - arcsin (0) + 2 πn : π + 2 πn

π - arcsin (0) + 2 πn

Utilizar la siguiente identidad trivial:

arcsin (0) = 0

x 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 arcsin (x) 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} arcsin (x) 0^{\circ} 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ}

= π - 0 + 2 πn

π - 0 + 2 πn = π + 2 πn

= π + 2 πn

4 x + 1 7^{\circ} < π + 2 πn

Desplace

1 7^{\circ}

a la derecha

4 x + 1 7^{\circ} < π + 2 πn

Restar

1 7^{\circ}

de ambos lados

4 x + 1 7^{\circ} - 1 7^{\circ} < π + 2 πn - 1 7^{\circ}

Simplificar

4 x < π + 2 πn - 1 7^{\circ}

4 x < π + 2 πn - 1 7^{\circ}

Dividir ambos lados entre

4

4 x < π + 2 πn - 1 7^{\circ}

Dividir ambos lados entre

4

\frac{4 x}{4} < \frac{π}{4} + \frac{2 πn}{4} - \frac{1 7 ^{\circ}}{4}

Simplificar

x < \frac{π}{4} + \frac{πn}{2} - \frac{1 7 ^{\circ}}{4}

Simplificar

\frac{π}{4} - \frac{1 7 ^{\circ}}{4} : \frac{π - 1 7 ^{\circ}}{4}

\frac{π}{4} - \frac{1 7 ^{\circ}}{4}

Aplicar la regla

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

= \frac{π - 1 7 ^{\circ}}{4}

x < \frac{π - 1 7 ^{\circ}}{4} + \frac{π}{2} n

x < \frac{π - 1 7 ^{\circ}}{4} + \frac{π}{2} n

Combinar los rangos

x > \frac{πn}{2} - \frac{1 7 ^{\circ}}{4} and x < \frac{π - 1 7 ^{\circ}}{4} + \frac{π}{2} n

Mezclar intervalos sobrepuestos

- \frac{1 7 ^{\circ}}{4} + \frac{π}{2} n < x < \frac{π - 1 7 ^{\circ}}{4} + \frac{π}{2} n

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