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Popular >

cos(θ)>0\land sin(θ)<0

Solución

cos (θ) > 0 and sin (θ) < 0

Solución

\frac{3 π}{2} + 2 πn < θ < 2 π + 2 πn

+2

Notación de intervalos

(\frac{3 π}{2} + 2 πn, 2 π + 2 πn)

Decimal

4.71238 \dots + 2 πn < θ < 6.28318 \dots + 2 πn

Pasos de solución

cos (θ) > 0 and sin (θ) < 0

cos (θ) > 0 : - \frac{π}{2} + 2 πn < θ < \frac{π}{2} + 2 πn

cos (θ) > 0

Para

cos (x) > a

, si

- 1 \leq a < 1

entonces

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

- arccos (0) + 2 πn < θ < arccos (0) + 2 πn

Simplificar

- arccos (0) : - \frac{π}{2}

- arccos (0)

Utilizar la siguiente identidad trivial:

arccos (0) = \frac{π}{2}

x - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 arccos (x) π \frac{5 π}{6} \frac{3 π}{4} \frac{2 π}{3} \frac{π}{2} \frac{π}{3} \frac{π}{4} \frac{π}{6} 0 arccos (x) 18 0^{\circ} 15 0^{\circ} 13 5^{\circ} 12 0^{\circ} 9 0^{\circ} 6 0^{\circ} 4 5^{\circ} 3 0^{\circ} 0^{\circ}

= - \frac{π}{2}

Simplificar

arccos (0) : \frac{π}{2}

arccos (0)

Utilizar la siguiente identidad trivial:

arccos (0) = \frac{π}{2}

x - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 arccos (x) π \frac{5 π}{6} \frac{3 π}{4} \frac{2 π}{3} \frac{π}{2} \frac{π}{3} \frac{π}{4} \frac{π}{6} 0 arccos (x) 18 0^{\circ} 15 0^{\circ} 13 5^{\circ} 12 0^{\circ} 9 0^{\circ} 6 0^{\circ} 4 5^{\circ} 3 0^{\circ} 0^{\circ}

= \frac{π}{2}

- \frac{π}{2} + 2 πn < θ < \frac{π}{2} + 2 πn

sin (θ) < 0 : - π + 2 πn < θ < 2 πn

sin (θ) < 0

Para

sin (x) < a

, si

- 1 < a \leq 1

entonces

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

- π - arcsin (0) + 2 πn < θ < arcsin (0) + 2 πn

Simplificar

- π - arcsin (0) : - π

- π - arcsin (0)

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

- π - 0 = - π

= - π

Simplificar

arcsin (0) : 0

arcsin (0)

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

- π + 2 πn < θ < 0 + 2 πn

Simplificar

- π + 2 πn < θ < 2 πn

Combinar los rangos

- \frac{π}{2} + 2 πn < θ < \frac{π}{2} + 2 πn and - π + 2 πn < θ < 2 πn

Mezclar intervalos sobrepuestos

\frac{3 π}{2} + 2 πn < θ < 2 π + 2 πn

Ejemplos populares

tan(θ)=1\land cos(θ)>0,csc(θ)

tan (θ) = 1 and cos (θ) > 0, csc (θ)

- 1 < sin (x) \leq 0

tan(θ)= 1/3 \land sin(θ)<0

tan (θ) = \frac{1}{3} and sin (θ) < 0

cot(θ)=2\land sec(θ)>= 0

cot (θ) = 2 and sec (θ) \geq 0

sin(θ)=-(sqrt(3))/2 \land cos(θ)>= 0

sin (θ) = - \frac{3}{2} and cos (θ) \geq 0