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Popular >

6cos(x)+4>0,0<= x<2pi

Solución

6 cos (x) + 4 > 0, 0 \leq x < 2 π

Solución

0 \leq x < arccos (- \frac{2}{3}) or 2 π - arccos (- \frac{2}{3}) < x < 2 π

+2

Notación de intervalos

[0, arccos (- \frac{2}{3})) \cup (2 π - arccos (- \frac{2}{3}), 2 π)

Notación decimal

0 \leq x < 2.30052 \dots or 3.98266 \dots < x < 6.28318 \dots

Pasos de solución

6 cos (x) + 4 > 0, 0 \leq x < 2 π

Mover

4

al lado derecho

6 cos (x) + 4 > 0

Restar

4

de ambos lados

6 cos (x) + 4 - 4 > 0 - 4

Simplificar

6 cos (x) > - 4

6 cos (x) > - 4

Dividir ambos lados entre

6

6 cos (x) > - 4

Dividir ambos lados entre

6

\frac{6 cos ( x )}{6} > \frac{- 4}{6}

Simplificar

\frac{6 cos ( x )}{6} > \frac{- 4}{6}

Simplificar

\frac{6 cos ( x )}{6} : cos (x)

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

Dividir:

\frac{6}{6} = 1

= cos (x)

Simplificar

\frac{- 4}{6} : - \frac{2}{3}

\frac{- 4}{6}

Aplicar las propiedades de las fracciones:

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

= - \frac{4}{6}

Eliminar los terminos comunes:

2

= - \frac{2}{3}

cos (x) > - \frac{2}{3}

cos (x) > - \frac{2}{3}

cos (x) > - \frac{2}{3}

Para

cos (x) > a

, si

- 1 \leq a < 1

entonces

- arccos (a) + 2 πn < x < arccos (a) + 2 πn

- arccos (- \frac{2}{3}) + 2 πn < x < arccos (- \frac{2}{3}) + 2 πn

Combinar los rangos

- arccos (- \frac{2}{3}) + 2 πn < x < arccos (- \frac{2}{3}) + 2 πn and 0 \leq x < 2 π

0 \leq x < arccos (- \frac{2}{3}) or 2 π - arccos (- \frac{2}{3}) < x < 2 π

Ejemplos populares

cos^{2} (x) > 0

cos (x) < 0.5

tan (x) < 0

cos(x)-sin(x)>0

cos (x) - sin (x) > 0

sin (2 x) < \frac{1}{2}