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Popular >

cos(θ)=0.222\land tan(θ)<0,sin(θ)

Solución

cos (θ) = 0.222 and tan (θ) < 0, sin (θ)

Falso para todo θ \in R

Pasos de solución

cos (θ) = 0.222 and tan (θ) < 0

cos (θ) = 0.222 : θ = 1.34693 \dots + 2 πn, θ = 2 π - 1.34693 \dots + 2 πn

cos (θ) = 0.222

Aplicar propiedades trigonométricas inversas

cos (θ) = 0.222

Soluciones generales para

cos (θ) = 0.222

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = 2 π - arccos (a) + 2 πn

θ = arccos (0.222) + 2 πn, θ = 2 π - arccos (0.222) + 2 πn

θ = arccos (0.222) + 2 πn, θ = 2 π - arccos (0.222) + 2 πn

Mostrar soluciones en forma decimal

θ = 1.34693 \dots + 2 πn, θ = 2 π - 1.34693 \dots + 2 πn

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

tan (θ) < 0

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

Combinar los rangos

(θ = 1.34693 \dots + 2 πn or θ = 2 π - 1.34693 \dots + 2 πn) and - \frac{π}{2} + πn < θ < πn

Mezclar intervalos sobrepuestos

Falso para todo θ \in R

sin (x) 0 \leq x \leq π

x = - 4 and csc (x) > 0

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

cosh (θ) = \frac{15}{4} and θ < 0, sinh (θ)

2 π > 3 tan (θ) + 1 \geq 0