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cos(θ)= 3/4 \land cot(θ)<0

Solução

cos (θ) = \frac{3}{4} and cot (θ) < 0

Falso para todo θ \in R

Passos da solução

cos (θ) = \frac{3}{4} and cot (θ) < 0

cos (θ) = \frac{3}{4} : θ = 0.72273 \dots + 2 πn, θ = 2 π - 0.72273 \dots + 2 πn

cos (θ) = \frac{3}{4}

Aplique as propriedades trigonométricas inversas

cos (θ) = \frac{3}{4}

Soluções gerais para

cos (θ) = \frac{3}{4}

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

θ = arccos (\frac{3}{4}) + 2 πn, θ = 2 π - arccos (\frac{3}{4}) + 2 πn

θ = arccos (\frac{3}{4}) + 2 πn, θ = 2 π - arccos (\frac{3}{4}) + 2 πn

Mostrar soluções na forma decimal

θ = 0.72273 \dots + 2 πn, θ = 2 π - 0.72273 \dots + 2 πn

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

cot (θ) < 0

cot (x) < a

então

arccot (a) + πn < x < π + πn

arccot (0) + πn < θ < π + πn

Simplificar

arccot (0) : \frac{π}{2}

arccot (0)

Utilizar a seguinte identidade trivial:

arccot (0) = \frac{π}{2}

x - 3 - 1 - \frac{3}{3} 0 \frac{3}{3} 13 arccot (x) \frac{5 π}{6} \frac{3 π}{4} \frac{2 π}{3} \frac{π}{2} \frac{π}{3} \frac{π}{4} \frac{π}{6} arccot (x) 15 0^{\circ} 13 5^{\circ} 12 0^{\circ} 9 0^{\circ} 6 0^{\circ} 4 5^{\circ} 3 0^{\circ}

= \frac{π}{2}

\frac{π}{2} + πn < θ < π + πn

Combinar os intervalos

(θ = 0.72273 \dots + 2 πn or θ = 2 π - 0.72273 \dots + 2 πn) and \frac{π}{2} + πn < θ < π + πn

Junte intervalos que se sobrepoem

Falso para todo θ \in R

sin (θ) > 0 and cos (θ) > 0

sin (4 θ) 0 \leq θ \leq π

[sin (π) t] 0 \leq t \leq 2

cosh (θ) = \frac{7}{3} and θ < 0, sinh (θ)

cos (x) \leq sin^{2} (x) \leq \frac{3}{2} sin (x)