Sinusoidal Functions Practice Test

A Ferris wheel height is $h(t)=10\cos\left(\frac{\pi}{12}t+\frac{\pi}{3}\right)+12$, with $t$ in minutes. The amplitude is the wheel radius, and the midline is the axle height. The phase shift indicates when the rider reaches the top relative to $t=0$. Using the given function, determine the phase shift of the function and explain its significance.​

A Ferris wheel height is given by $h(t)=14\cos!\left(\frac{\pi}{30}t-\frac{\pi}{3}\right)+16$, with $t$ in seconds. The amplitude is $14$ feet and the vertical shift is $16$ feet. The seat oscillates between $30$ feet and $2$ feet. The phase shift moves the first maximum away from $t=0$. Using the given function, determine the phase shift of the function and explain its significance.