Evaluate the function \( f(x)=-\sin x \) at \( x=\frac{3 \pi}{2} .(1 \) point) \( \left(\frac{3 \pi}{2}, \square\right) \)

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

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

What is the general equation of a cosine function with an amplitude of 3 , a period of \( 4 \pi \), and a horizontal shift of \( -\pi \) ? \( \begin{array}{l}y=4 \pi \cos (3(x-\pi)) \\ y=3 \cos (4 \pi(x+\pi)) \\ y=3 \cos (0.5(x+\pi)) \\ y=4 \pi \cos (0.2(x+\pi))\end{array} \)

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