\( \begin{array}{l}\text { Determine para qué valores de } x \in(0,2 \pi) \text { se } \\ \text { cumple: }\end{array} \) \( \left\lvert\, \frac{\cot ^{2}(x)+4}{2 \operatorname{sen}^{2}(x)+5 \operatorname{sen}(x)-3}>0\right. \)

Solve the equation for exact solutions over the interval \( [0,2 \pi) \) \( 2 \tan 3 x=2 \) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is \( \left\{\frac{\pi}{12}, \frac{5 \pi}{12}, \frac{3 \pi}{4}, \frac{13 \pi}{12}, \frac{17 \pi}{12}, \frac{7 \pi}{4}\right\} \). (Type an exact answer, using \( \pi \) as needed. Type your answer in radians. Use integers or fractions for any numbers in the expression. Use a com B. The solution is the empty set.

6 A plane flies on a true bearing of \( 280^{\circ} \mathrm{T} \) at \( 600 \mathrm{~km} / \mathrm{h} \) after taking off at 1300 hours. To the nearest kilometre, how far north of its starting position is it at 1530 hours?

Solve \( \sin ^{2}(t)=-8 \cos (t) \) for all solutions \( 0 \leq t<2 \pi \)

When evaluating the expression \( \tan ^{-1}\left(-\frac{\sqrt{3}}{3}\right) \), the angle obtained is ...

(d) Quando fazemos determinaçōes experimentais de uma grandeza \( X \), representamos seu valor numérico final acompanhado do erro \( \Delta X \) associado à medida, na forma \( X \pm \Delta X \). Para calcularmos o valor de uma funçāo \( f(X \pm \Delta X) \), utilizamos a regra \[ f(X \pm \Delta X)=f(X) \pm f^{\prime}(X) \Delta X \] Obtenha as fórmulas referentes a (i) \( \sin (X \pm \Delta X) \) e (ii) \( \cos (X \pm \Delta X) \)