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Popular >

sin(θ)= 2/3 \land tan(θ)>0

Solución

sin (θ) = \frac{2}{3} and tan (θ) > 0

θ = 0.72972 \dots + 2 πn

Notación de intervalos

θ = 0.72972 \dots + 2 πn

Pasos de solución

sin (θ) = \frac{2}{3} and tan (θ) > 0

sin (θ) = \frac{2}{3} : θ = 0.72972 \dots + 2 πn, θ = π - 0.72972 \dots + 2 πn

sin (θ) = \frac{2}{3}

Aplicar propiedades trigonométricas inversas

sin (θ) = \frac{2}{3}

Soluciones generales para

sin (θ) = \frac{2}{3}

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

θ = arcsin (\frac{2}{3}) + 2 πn, θ = π - arcsin (\frac{2}{3}) + 2 πn

θ = arcsin (\frac{2}{3}) + 2 πn, θ = π - arcsin (\frac{2}{3}) + 2 πn

Mostrar soluciones en forma decimal

θ = 0.72972 \dots + 2 πn, θ = π - 0.72972 \dots + 2 πn

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

tan (θ) > 0

tan (x) > a

entonces

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

arctan (0) + πn < θ < \frac{π}{2} + 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

0 + πn < θ < \frac{π}{2} + πn

Simplificar

πn < θ < \frac{π}{2} + πn

Combinar los rangos

(θ = 0.72972 \dots + 2 πn or θ = π - 0.72972 \dots + 2 πn) and πn < θ < \frac{π}{2} + πn

Mezclar intervalos sobrepuestos

θ = 0.72972 \dots + 2 πn

cos (θ) < 0 and tan (θ) > 0

cosh (θ) = \frac{29}{8} and θ < 0, sinh (θ)

0 < arcsin (y) < π

- 1 \leq cos (x) \leq 1

- \frac{π}{2} < arctan (y) < 0