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Popular >

sin(θ)<0\land cot(θ)<0

Solución

sin (θ) < 0 and cot (θ) < 0

Solución

Falso para todo θ \in R

Pasos de solución

sin (θ) < 0 and cot (θ) < 0

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

cot (θ) < 0 : \frac{π}{2} + πn < θ < π + πn

cot (θ) < 0

Pi

cot (x) < a

entonces

arccot (a) + πn < x < π + πn

arccot (0) + πn < θ < π + πn

Simplificar

arccot (0) : \frac{π}{2}

arccot (0)

Utilizar la siguiente identidad trivial:

arccot (0) = \frac{π}{2}

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

= \frac{π}{2}

\frac{π}{2} + πn < θ < π + πn

Combinar los rangos

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

Mezclar intervalos sobrepuestos

Falso para todo θ \in R

Ejemplos populares

5<= 20cos(pi/(20)(x-20))+23<= 20

5 \leq 20 cos (\frac{π}{20} (x - 20)) + 23 \leq 20

tan(θ)=-1\land sin(θ)>0

tan (θ) = - 1 and sin (θ) > 0

sin(x/2-pi/3)0<= x<= 2pi

sin (\frac{x}{2} - \frac{π}{3}) 0 \leq x \leq 2 π

cos(θ)= 1/4 \land 0>θ>90,tan(θ)

cos (θ) = \frac{1}{4} and 0^{\circ} > θ > 9 0^{\circ}, tan (θ)

cot(θ)=-sqrt(2)\land cos(θ)>0

cot (θ) = - 2 and cos (θ) > 0