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

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

   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 = 30 cos(πt/30) + 150
   • h = 15 cos(πt/30) + 150
   • h = 15 cos(πt/15) + 150
   • h = 15 sin(πt/30) + 150
4. 4.

   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
5. 5.

   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
6. 6.

   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
7. 7.

   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.
   • The middle water level is 4 ft.
   • High tide is 4 ft.
   • One tide cycle takes 4 hours.
8. 8.

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

   • 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.
   • The top seat is 15 m up.
9. 9.

   Ren's daylight model for a town in Arizona is d = 2 sin(π(t − 3)/6) + 12, with d in hours and t the month number. What does the 2 tell Ren?

   • The longest and shortest days differ by 2 hours.
   • The longest day is 2 hours more than average.
   • The longest day has 2 hours of daylight.
   • The cycle repeats every 2 months.
10. 10.

    Zee's bike valve model is h = 30 sin(πt) + 33, with h in cm. What does the 33 tell Zee?

    • The valve's highest point is 33 cm.
    • The valve goes 33 cm above the center.
    • The center of the wheel is 33 cm up.
    • The wheel turns 33 times a minute.