Q1. Solve the following equations on the interval \( [0,2 \pi) \). \( \begin{array}{ll}\text { a. } 2 \cos x=1 & \text { b. } \sin (2 x)=\cos (x) \\ \text { Hint: } \operatorname{Recall} \sin (2 x)=2 \sin (x) \cos (x)\end{array} \) \( \begin{array}{ll}\text { c. } \csc ^{2}(x)-4=0 & \text { d. } 2(\tan (x)+3)=5+\tan (x)\end{array} \)

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?

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

(1) จงหาค่าของ \( 2 \sin 20^{\circ}+\cot 68^{\circ} \)

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