Periodic Modeling Worksheets Grade 11

1. Aroha is monitoring the height of a Ferris wheel car above the ground. The Ferris wheel has a diameter of 36 meters and its boarding platform is 3 meters above the ground. The wheel completes one full revolution every 40 seconds. At time t = 0 seconds, Aroha boards the car at the lowest point of the wheel. Write a sine function of the form h(t) = A sin(Bt + C) + D that models the height of the car above the ground (in meters) as a function of time t (in seconds). Then, determine the height of the car above the ground after 10 seconds.
2. Emma is tracking the height of a Ferris wheel seat. The maximum height is 75 meters, the minimum height is 15 meters, and it completes one full revolution every 18 minutes. If the seat starts at its minimum height, write the trigonometric function for the height h(t) in meters after t minutes.
3. Mere is modeling the height of a Ferris wheel car above the ground. The wheel has diameter 30 meters, the bottom of the wheel is 2 meters above the ground, and it completes one revolution every 90 seconds. If a car starts at the 3 o'clock position, write the trigonometric function h(t) for the car's height after t seconds.

…and 3 more problems

1. Olivia is tracking the number of hours of daylight in a northern city. The maximum daylight is 15 hours on June 21 (day 172 of the year), and the minimum daylight is 9 hours on December 21 (day 355). Write a sine function D(t) that models the daylight hours as a function of day number t (t = 0 corresponds to January 1). Then, determine the first day after January 1 when the daylight reaches 12 hours.
2. sin²(π/4) + cos²(π/4) = ?
3. A Ferris wheel with a diameter of 40 meters completes one full revolution every 2 minutes. When boarding, passengers step onto a platform that is 2 meters above ground level at the lowest point of the wheel. If Liam boards the Ferris wheel at time t=0, write a trigonometric function h(t) that models his height above ground in meters as a function of time in minutes.

…and 4 more problems

1. sin²(π/6) + cos²(π/6) = ?
2. Ava is modeling the height of ocean waves. The waves oscillate between a maximum height of 16 feet and a minimum height of 6 feet, with a period of 11 seconds. If she models the height h (in feet) as a function of time t (in seconds) using a sine function starting at the average height and increasing, what is the function h(t)?
3. Ava is modeling the height of a Ferris wheel seat above ground. The maximum height is 61 meters, minimum height is 16 meters, and it completes one revolution every 6 minutes. At t=0, the seat is at its minimum height. Write the function h(t) = A sin(Bt + C) + D.

…and 4 more problems