th Sketching the Graph of a Trigonometric Function hs In Exercises 15-38, sketch the graph of the function. (Include two full periods.) \( \begin{array}{ll}\text { 15. } y=\frac{1}{3} \tan x & \text { 16. } y=\tan 4 x \\ \text { 17. } y=-2 \tan 3 x & \text { 18. } y=-3 \tan \pi x \\ \text { 19. } y=-\frac{1}{2} \sec x & \text { 20. } y=\frac{1}{4} \sec x \\ \text { 21. } y=\csc \pi x & \text { 22. } y=3 \csc 4 x\end{array} \)

A salvage vessel locates a sunken ship 168 m below the water's surface. It determines that the angle of depression to one end of the ship is \( 47.6^{\circ} \) and to the other end is \( 65.1^{\circ} \). Determine the length of the ship.

A periodic function passes through the origin and then descends to a minimum of \( -\frac{2}{3} \) when \( x=\frac{\pi}{2} \). It passes through the x-axis again when \( x=\pi \) and rises to a maximum of \( \frac{2}{3} \) when periodic function? (1 point) \( y=-\frac{2}{3} \cos x \) \( y=\frac{2}{3} \sin x \) \( y=\frac{4}{3} \sin x \) \( y=-\frac{2}{3} \sin x \)

Rewrite the cosine function \( f(x)=-3 \cos \left(x-\frac{\pi}{8}\right)+2 \) as a translated sine function. \( \begin{array}{l}\text { (1 point) } \\ f(x)=-3 \sin \left(x+\frac{\pi}{4}\right)+2 \\ f(x)=-3 \sin \left(x+\frac{\pi}{24}\right)+2 \\ f(x)=-3 \sin \left(x+\frac{3 \pi}{8}\right)+2 \\ f(x)=-3 \sin \left(x-\frac{5 \pi}{8}\right)+2\end{array} \)

When the function \( f(x)= \) sin \( x \) is reflected across the \( y \)-axis, identify the coordinates of the reflected point of \( \left(\frac{\pi}{2}, 1\right) \) across the \( y \)-axis. (1 point) \( \left(\frac{-\pi}{2},-1\right) \) \( \left(\frac{-\pi}{2}, 1\right) \) \( \left(\frac{\pi}{2},-1\right) \) \( \left(\frac{\pi}{2}, 1\right) \)

Determine the period of the function \( f(x)=2 \cos \left(\frac{1}{6} x+\frac{\pi}{3}\right) \). (1 point) \( -\frac{\pi}{3} \) \( \frac{\pi}{3} \) \( 2 \pi \) \( 12 \pi \)