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Popular Trigonometria >

tan(θ)<0\land sin(θ)>0

Solução

tan (θ) < 0 and sin (θ) > 0

Solução

- \frac{π}{2} + πn < θ < πn

+2

Notação de intervalo

(- \frac{π}{2} + πn, πn)

Decimal

- 1.57079 \dots + πn < θ < πn

Passos da solução

tan (θ) < 0 and sin (θ) > 0

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

tan (θ) < 0

Se

tan (x) < a

então

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

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

Simplificar

arctan (0) : 0

arctan (0)

Utilizar a seguinte identidade 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

sin (θ) > 0 : 2 πn < θ < π + 2 πn

sin (θ) > 0

Para

sin (x) > a

, se

- 1 \leq a < 1

então

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

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

Simplificar

arcsin (0) : 0

arcsin (0)

Utilizar a seguinte identidade 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

Simplificar

π - arcsin (0) : π

π - arcsin (0)

Utilizar a seguinte identidade 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

0 + 2 πn < θ < π + 2 πn

Simplificar

2 πn < θ < π + 2 πn

Combinar os intervalos

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

Junte intervalos que se sobrepoem

- \frac{π}{2} + πn < θ < πn

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