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Popular >

tan(θ)<0\land cos(θ)>0

Solución

tan (θ) < 0 and cos (θ) > 0

Solución

Falso para todo θ \in R

Pasos de solución

tan (θ) < 0 and cos (θ) > 0

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

tan (θ) < 0

Pi

tan (x) < a

entonces

- \frac{π}{2} + πn < x < arctan (a) + πn

- \frac{π}{2} + πn < θ < arctan (0) + πn

Simplificar

arctan (0) : 0

arctan (0)

Utilizar la siguiente identidad trivial:

arctan (0) = 0

x 0 \frac{3}{3} 13 arctan (x) 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} arctan (x) 0^{\circ} 3 0^{\circ} 4 5^{\circ} 6 0^{\circ}

= 0

- \frac{π}{2} + πn < θ < 0 + πn

Simplificar

- \frac{π}{2} + πn < θ < 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

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

Mezclar intervalos sobrepuestos

Falso para todo θ \in R

Ejemplos populares

sec(θ)= 4/3 \land cot(θ)<0

sec (θ) = \frac{4}{3} and cot (θ) < 0

0<cos(x)<sin(x)

0 < cos (x) < sin (x)

1/2 <sin(θ)<(sqrt(3))/2

\frac{1}{2} < sin (θ) < \frac{3}{2}

(x^2)/(sqrt(2))-sin^2(x)in^0<x<2pi

\frac{x ^{2}}{2} - sin^{2} (x) i n^{0} < x < 2 π

tan(θ)=-4/5 \land cos(θ)>0

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