\begin{tabular}{l} Question 1 \\ Find the lengths of the missing sides if side \( a \) is opposite angle A , side b is opposite angle B , and side c is the hypotenuse. \\ \( \begin{array}{l}A=\frac{5}{12}, b=6 \\ \mathrm{O}=2.5, \mathrm{c}=6.5 \\ \mathrm{a}=3, \mathrm{c}=7 \\ \mathrm{O}=2, \mathrm{c}=6 \\ \mathrm{O}=6.5, \mathrm{c}=2.5\end{array} \) \\ \hline\end{tabular}

What is the period of \( y=\sin (3 x) \) ? \( \begin{array}{l}\frac{\pi}{3} \\ \frac{2 \pi}{3} \\ 3 \pi \\ 6 \pi\end{array} \)

A buoy starts at a height of 0 in relation to sea level and then goes up. Its maximum displacement in either direction is 6 feet, and the time it takes to go from its highest point to its lowest point is 4 seconds. Which of the following equations can be used to model \( h \), the height in feet of the buoy in relation to sea level as a function of time, \( t \), in seconds? \( h=4 \sin \left(\frac{\pi}{6} t\right) \) \( h=4 \sin \left(\frac{\pi}{3} t\right) \) \( h=6 \sin \left(\frac{\pi}{4} t\right) \) \( h=6 \sin \left(\frac{\pi}{2} t\right) \)

The displacement, \( d \), in millimeters of a tuning fork as a function of time, \( t \), in seconds can be modeled with the equation \( d=0.4 \sin (1760 \pi f) \). What is the maximum displacement of the tuning fork? 0.2 mm 0.4 mm 0.8 mm 2.5 mm

Which transformations are needed to change the parent cosine function to \( y=3 \cos (10(x-\pi)) \) ? vertical compression of 3 , horizontal stretch to a period of \( 5 \pi \), phase shift of \( \pi \) units to the left vertical stretch of 3 , horizontal compression to a period of \( \frac{\pi}{5} \), phase shift of \( \pi \) units to the right vertical compression of 3 , horizontal stretch to a period of 10 p, phase shift of \( \pi \) units to the right vertrech of 3 , horizontal compression to a period of \( \frac{\pi}{5} \), phase shift of \( \pi \) units to the left

8. The teminal amm for angle \( \theta \) passes through the point \( (7,-6) \). a) Determine the exact simplified ralues of the 6 trigonometric ratios, inolube a diagram.