If \( \csc \theta=\frac{\sqrt{125}}{10} \), what is \( \tan \theta ? \)

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?

A pylon \( \$ \$ 23.7 \$ \$ \mathrm{~m} \) high casts a shadow \( \$ \$ 46.8 \$ \$ \mathrm{~m} \) long. Determine the angle of elevation of the sun to the nearest tenth of a degree. 23.7 m high casts a shadow 46.8 m long. Determine the angle of elevation of the sun to the nearest tenth of a degree. Show answer

(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) \( \cos (X \pm \Delta X) \)

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

4) \( \operatorname{Si} \tan \Phi=\frac{\sqrt{6}}{3} \), donde " \( \Phi \) " es un ángulo agudo, calcular: \( \mathrm{P}=\sqrt{3} \operatorname{Sec} \Phi+\sqrt{2} \operatorname{Csc} \Phi \)