Model a repeating situation with a trig function
Grade 11 Math Worksheet
Circle the best answer, or write your answer on the line.
t (hours after midnight) = 0, 3, 6, 9, 12; h (feet) = 4, 6, 4, 2, 4. Ren records the tide at a harbor. Which model matches every row of the table?
- h = 4 sin(πt/6) + 4
- h = 2 sin(πt/6) + 4
- h = 2 cos(πt/6) + 4
- h = 2 sin(12t) + 4
t (minutes) = 0, 1, 2, 3, 4; h (meters) = 2, 12, 22, 12, 2. Zee watches one seat of a Ferris wheel from the ground. Which model matches every row of the table?
- h = -10 cos(πt/2) + 12
- h = 10 cos(πt/2) + 12
- h = -10 cos(πt/2)
- h = -10 cos(4t) + 12
t (seconds) = 0, 3/4, 3/2, 9/4, 3; d = -1, 0, 1, 0, -1. Ari times a playground swing; d is meters in front of the rest point. Which model matches every row of the table?
- d = -cos(3t)
- d = -2 cos(2πt/3)
- d = cos(2πt/3)
- d = -sin(2πt/3)
- d = -cos(2πt/3)
t (seconds) = 0, 1/2, 1, 3/2, 2; h (cm) = 33, 63, 33, 3, 33. Bo walks a bike and tracks the tire valve. Which model matches every row of the table?
- h = 30 sin(πt)
- h = 30 sin(πt) + 33
- h = 30 cos(πt) + 33
- h = 30 sin(2t) + 33
Esme walks a bike; the tire valve goes around once every 2 seconds. In h = 30 sin(☐t) + 33, what number goes in the box, in terms of π?
Jun sees a Ferris wheel turn once every 6 minutes. In h = -15 cos(☐t) + 17, what number goes in the box, in terms of π?
Kira's harbor has a tide cycle every 12 hours. In h = 3 cos(☐t) + 4, what number goes in the box, in terms of π?
Milo's tide model is h = 4 sin(πt/6) + 5, with t in hours. When does the water first reach its highest, in hours?
Noah's bike valve model is h = -30 sin(πt) + 33, with t in seconds. When does the valve first reach its highest, in seconds?
Ren's swing model is d = -sin(2πt/3), with t in seconds. When is the swing first farthest forward, in seconds?
