Model a repeating situation with a trig function

Answer Key - Grade 11 Math Worksheet

Circle the best answer, or write your answer on the line.

1. 1.

   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 sin(12t) + 4
   • h = 2 cos(πt/6) + 4
2. 2.

   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)
   • h = -10 cos(πt/2) + 12
   • h = -10 cos(4t) + 12
   • h = 10 cos(πt/2) + 12
3. 3.

   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 = -2 cos(2πt/3)
   • d = cos(2πt/3)
   • d = -cos(3t)
   • d = -cos(2πt/3)
   • d = -sin(2πt/3)
4. 4.

   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) + 33
   • h = 30 sin(πt)
   • h = 30 cos(πt) + 33
   • h = 30 sin(2t) + 33
5. 5.

   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?

   π
6. 6.

   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?

   π/3
7. 7.

   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?

   π/6
8. 8.

   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?

   3
9. 9.

   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?

   3/2
10. 10.

    Ren's swing model is d = -sin(2πt/3), with t in seconds. When is the swing first farthest forward, in seconds?

    9/4