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?

Solve the equation for \( x \), where \( x \) is restricted to the given interval. \( y=8 \csc 4 x \), for \( x \) in \( \left[-\frac{\pi}{8}, 0\right) \cup\left(0, \frac{\pi}{8}\right] \)

A ship travels on a bearing of \( 300^{\circ} \) for 3 hours at a speed of 10 knots per hour ( \( 1 \mathrm{knot}= \) 1 nautical mile per hour). It then travels at a bearing of \( 200^{\circ} \) and continues at 10 knots per hour for 3 hours. How many nautical miles is the ship from its starting point? Round to the nearest mile.

A. \( \arccos \left(-\frac{\sqrt{2}}{2}\right)=x \)

C. \( \arcsin \frac{\sqrt{2}}{2}=x \)

Part 3 of 3 Use the given information to find (a) \( \sin (s+t) \), (b) tan \( (s+t) \), and \( (\mathrm{c}) \) the quadrant of \( s+t \). 0.33 of 1 \( \sin \mathrm{~s}=\frac{4}{7} \) and \( \sin \mathrm{t}=-\frac{1}{7} \), s in quadrant II and t in quadrant IV