Model a repeating situation with a trig function

Answer Key - Grade 11 Math Worksheet - Challenge Me

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

1. 1.

   Zee's harbor has high tide 7 ft at midnight and the next low tide, 1 ft, at 6 AM. With t hours after midnight, which model fits?

   • h = 3 cos(πt/3) + 4
   • h = 6 cos(πt/6) + 4
   • h = 3 cos(πt/6) + 4
   • h = 3 sin(πt/6) + 4
2. 2.

   Ari watches a Ferris wheel seat: 2 m up at the bottom, then 32 m up at the top 2 minutes later. With t minutes, which model fits?

   • h = -15 cos(πt) + 17
   • h = -30 cos(πt/2) + 17
   • h = 15 cos(πt/2) + 17
   • h = -15 cos(πt/2) + 17
3. 3.

   Bo's town has 9 hours of daylight at the December solstice and 15 hours six months later. With t months after the solstice, which model fits?

   • d = -3 cos(πt/3) + 12
   • d = -6 cos(πt/6) + 12
   • d = 3 cos(πt/6) + 12
   • d = -3 cos(πt/6) + 12
4. 4.

   Esme's wall clock: the minute-hand tip is 165 cm up at the 12 and 135 cm up at the 6, 30 minutes later. With t minutes after the hour, which model fits?

   • h = 15 sin(πt/30) + 150
   • h = 15 cos(πt/30) + 150
   • h = 30 cos(πt/30) + 150
   • h = 15 cos(πt/15) + 150
5. 5.

   Jun's daylight model is d = 3 sin(π(t − 3)/6) + 12, with t the month number (March is 3). What is d at t = 4, in hours?

   27/2
6. 6.

   Kira's daylight model is d = -3 cos(πt/6) + 12, with t months after the December solstice. What is d at t = 2, in hours?

   21/2
7. 7.

   Luz's tide model is h = 3 cos(π(t − 2)/6) + 4, with t hours after midnight. What is h at t = 4, in feet?

   11/2
8. 8.

   Milo's Ferris wheel seat model is h = -15 cos(πt/3) + 17, with t in minutes. What is h at t = 1, in meters?

   19/2
9. 9.

   Noah's tide model is h = 3 cos(πt/6) + 4, with h in feet. What does the 4 tell Noah?

   • The water rises 4 ft above its middle level.
   • One tide cycle takes 4 hours.
   • High tide is 4 ft.
   • The middle water level is 4 ft.
10. 10.

    Pia's Ferris wheel seat model is h = -15 cos(πt/2) + 17, with h in meters. What does the 15 tell Pia?

    • The top seat is 15 m up.
    • The hub is 15 m up.
    • A seat goes 15 m above and below the hub.
    • A seat rises 15 m from the bottom to the top.