GW Score: \( 12 \%, 6 \) of 50 points A ship is sailing due north. At a certain point, the bearing of a lighthouse 4.9 km away is \( \mathrm{N} 38.5^{\circ} \mathrm{E} \). Later on, the captain notices that the bearing of the lighthouse has become \( \mathrm{S} 33.2^{\circ} \mathrm{E} \). How far did the ship travel between the two observations of the lighthouse?

\( 179 ^ { \circ } 59 ^ { \prime } 60 ^ { \prime \prime } - 103 ^ { \circ } 31 ^ { \prime } 14 ^ { \prime \prime } \)

If \( \tan \left(3 \theta-70^{\circ}\right) \times \tan \theta=1 \) where \( \left.\theta \in\right] 0, \frac{\pi}{3}[ \), then \( \sin (2 \theta+10)= \)

Which of the following correctly describes the phase shift of the function \( f(x)=2 \sin \left(x+\frac{\pi}{6}\right) \) ? (1 point) \( 0 . \frac{\pi}{6} \) \( \frac{\pi}{2} \)

Find the period and write the equation of the sine function that has a maximum at \( \left(\frac{\pi}{14}, 1\right) \) and a minimum at \( \left(\frac{3 \pi}{14},-1\right) \). (1 point) period \( =\square \) \( f(x)=\sin (\square) \)

\( 179 ^ { \circ } 59 ^ { \prime } 60 ^ { \prime \prime } - 103 ^ { \circ } 31 ^ { \prime } 14 ^ { \prime \prime } \)