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Popular >

tan(θ)=-4/5 \land cos(θ)>0,csc(θ)

Solución

tan (θ) = - \frac{4}{5} and cos (θ) > 0, csc (θ)

Falso para todo θ \in R

Pasos de solución

tan (θ) = - \frac{4}{5} and cos (θ) > 0

tan (θ) = - \frac{4}{5} : θ = - 0.67474 \dots + πn

tan (θ) = - \frac{4}{5}

Aplicar propiedades trigonométricas inversas

tan (θ) = - \frac{4}{5}

Soluciones generales para

tan (θ) = - \frac{4}{5}

tan (x) = - a \Rightarrow x = arctan (- a) + πn

θ = arctan (- \frac{4}{5}) + πn

θ = arctan (- \frac{4}{5}) + πn

Mostrar soluciones en forma decimal

θ = - 0.67474 \dots + πn

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

Combinar los rangos

θ = - 0.67474 \dots + πn and - \frac{π}{2} + 2 πn < θ < \frac{π}{2} + 2 πn

Mezclar intervalos sobrepuestos

Falso para todo θ \in R

- \frac{1}{2} < cos (x) < \frac{1}{2}

sin (θ) > 0 and cos (θ) < 0

sin (θ) < 0 and (csc (θ)) (cos (θ)) > 0

cosh (θ) = \frac{12}{7} and θ < 0, sinh (θ)

0 \leq sin^{2} (x) \leq 1