This quiz covers sections 5.1 to 5.3 . The allowable time is 90 minutes. 1 Multiple Choice 1 point Find the exact value of \( \tan 2 \theta \), given that \( \cos \theta=-\frac{\sqrt{5}}{5}, \sin \theta>0 \). \( \frac{3}{5} \)

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

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

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

5. Se observa un semáforo desde la ventana de un edificio, a 30 m del suelo. El ángulo de depresión para observar la parte superior del semáforo es de \( 70^{\circ} \), mientras que el ángulo de depresión para observar su base mide \( 88^{\circ} \). ¿Cuál es la altura del semáforo?

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? \( h=4 \sin \left(\frac{\pi}{6} t\right) \) \( h=4 \sin \left(\frac{\pi}{3} t\right) \) \( h=6 \sin \left(\frac{\pi}{4} t\right) \) \( h=6 \sin \left(\frac{\pi}{2} t\right) \)