Model a repeating situation with a trig function

Answer Key - Grade 11 Math Worksheet - Building Confidence

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

1. 1.

   t (hours after midnight) = 0, 3, 6, 9, 12; h (feet) = 9, 5, 1, 5, 9. Milo records the tide at a harbor. By how many feet does the water rise above its middle level?

   4
2. 2.

   t (minutes) = 0, 2, 4; h (meters) = 2, 32, 2. Pia watches one seat of a Ferris wheel from the ground. What is the midline height, in meters?

   17
3. 3.

   t (seconds) = 0, 1, 2; h (cm) = 3, 63, 3. Ren walks a bike and tracks the tire valve. What is the midline height, in cm?

   33
4. 4.

   t (hours after midnight) = 2, 5, 8, 11, 14; h (feet) = 7, 4, 1, 4, 7. Zee records the tide at a harbor. How many hours does one full tide cycle take?

   12
5. 5.

   Bo's tide model is h = 3 sin(πt/6) + 4, with t in hours. What is h at t = 9, in feet?

   1
6. 6.

   Esme's classroom clock model is h = 15 cos(πt/30) + 150, with t in minutes. What is h at t = 30, in cm?

   135
7. 7.

   Jun's Ferris wheel seat model is h = -16 cos(πt/3) + 18, with t in minutes. What is h at t = 3, in meters?

   34
8. 8.

   Kira's bike valve model is h = -30 sin(πt) + 33, with t in seconds. What is h at t = 3/2, in cm?

   63
9. 9.

   Luz sees a Ferris wheel whose lowest seat is 4 m up and whose top seat is 36 m up. How high is the midline, in meters?

   20
10. 10.

    Noah reads a tide chart: high tide is 8 ft and low tide is 2 ft. What is the midline, in feet?

    5