True or False 1 point Verify that \( \frac{1}{1+\sin t}+\frac{1}{1-\sin t}=2 \cos ^{2} t \) is an identity. True False

Starting at its rightmost position, it takes 2 seconds for the pendulum of a grandfather clock to swing a horizontal distance of 18 inches from right to left and 2 seconds for the pendulum to swing back from left to right. Which of the following equations models \( d \), the horizontal distance in inches of the pendulum from the center as a function of time, \( t \), in seconds? Assume that right of center is a positive distance and left of center is a negative distance. \( d=9 \cos \left(\frac{\pi}{4} t\right) \) \( d=9 \cos \left(\frac{\pi}{2} t\right) \) \( d=18 \cos \left(\frac{\pi}{4} t\right) \) \( d=18 \cos \left(\frac{\pi}{2} t\right) \)

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

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

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.

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