A roller coaster's height from the ground is modeled by r(t) = 4sin(4t)+25 where t is time in minutes. A Ferris wheel's height from the ground is modeled by f(t) = -8cos(3t)+30 where t is time in minutes. Assuming each ride is roughly 4 minutes long and they begin at the same time, determine when the rides are at the same height throughout the duration of the ride. 1. Write an equation that describes the instances when the rides are at the same height.
2. Solve this equation on the appropriate interval. (Hint: Use the length of the ride from start to finish.)