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 hypotenus \( \begin{array}{l}A=\frac{5}{12}, b=6\end{array} \)

Prove the following trigonometric identity: \( \frac{\sin A\left[1-\sin \left(360^{\circ}-A\right)\right]}{1-\cos ^{2}\left(180^{\circ}+A\right)}-1=\operatorname{cosec} A \)

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 equation \( h=7 \sin \left(\frac{\pi}{21} t\right)+28 \) can be used to model the height, \( h \), in feet of the end of one blade of a windmill turning on an axis above the ground as a function of time, \( t \), in seconds. How long is the blade? Assume that the blade is pointing to the right, parallel to the ground, at \( t=0 \), and that the windmill turns counterclockwise at a constant rate. 7 feet 14 feet 21 feet 28 feet

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.

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