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Popular >

csc(x)=4\land cot(x)<0

Solución

csc (x) = 4 and cot (x) < 0

Solución

x = π - 0.25268 \dots + 2 πn

+1

Notación decimal

x = 2.88891 \dots + 2 πn

Pasos de solución

csc (x) = 4 and cot (x) < 0

csc (x) = 4 : x = 0.25268 \dots + 2 πn, x = π - 0.25268 \dots + 2 πn

csc (x) = 4

Aplicar propiedades trigonométricas inversas

csc (x) = 4

Soluciones generales para

csc (x) = 4

csc (x) = a \Rightarrow x = arccsc (a) + 2 πn, x = π - arccsc (a) + 2 πn

x = arccsc (4) + 2 πn, x = π - arccsc (4) + 2 πn

x = arccsc (4) + 2 πn, x = π - arccsc (4) + 2 πn

Mostrar soluciones en forma decimal

x = 0.25268 \dots + 2 πn, x = π - 0.25268 \dots + 2 πn

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

cot (x) < 0

Pi

cot (x) < a

entonces

arccot (a) + πn < x < π + πn

arccot (0) + πn < x < 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 < x < π + πn

Combinar los rangos

(x = 0.25268 \dots + 2 πn or x = π - 0.25268 \dots + 2 πn) and \frac{π}{2} + πn < x < π + πn

Mezclar intervalos sobrepuestos

x = π - 0.25268 \dots + 2 πn

Ejemplos populares

cos(x^2)0<x<sqrt(x)

cos (x^{2}) 0 < x < x

sin(x)=-4/5 \land cos(x)<0,sin(2x)

sin (x) = - \frac{4}{5} and cos (x) < 0, sin (2 x)

cos(θ)= 3/7 \land sin(θ)>0

cos (θ) = \frac{3}{7} and sin (θ) > 0

cosh(θ)= 26/7 \land θ<0,sinh(θ)

cosh (θ) = \frac{26}{7} and θ < 0, sinh (θ)

-pi/2 <arcsin(x)< pi/2

- \frac{π}{2} < arcsin (x) < \frac{π}{2}