Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.

Lesson: Modelling with Trigonometric Functions

Worksheet: Modelling with Trigonometric Functions • 13 Questions


Angela is jumping on a trampoline. Her height above the trampoline , in meters, is given by , at seconds after she started jumping.

How many seconds after each rebound does it take her to reach a height of 50 cm during the descent? Round your answer to the nearest tenth of a second.

  • A1.7 s
  • B0.3 s
  • C3.3 s
  • D2.6 s
  • E0.7 s

What fraction of the time is Angela at least 1.2 m above the trampoline? Express your answer as a percentage correct to one decimal place.

  • A
  • B
  • C
  • D
  • E


The outside temperature (in degrees Celsius) on a certain day was modeled with , where is the time after midnight in hours. At what times of the day was the temperature ? Give your answer to the nearest minute using a 24-hour format.

  • A17:06, 2:54
  • B8:54, 11:06
  • C8:54, 23:06
  • D20:54, 23:06
  • E11:06, 20:54


The daily solar irradiation on a point just above Earth’s atmosphere days after the summer solstice is given by . How many times per year is the daily solar irradiation W/m2? How many days after the solstice does this occur?

  • Atwice, after 196 and 352 days
  • Btwice, after 261 and 287 days
  • Ctwice, after 104 and 261 days
  • Dtwice, after 79 and 104 days
  • Etwice, after 79 and 287 days


The number of hours of daylight in Paris depends on the season, and it is modeled by , where is the number of the day in a year (January 1 is day 1). According to this model, when is the length of the day in Paris 10 hours?

  • AJanuary 20, May 22
  • BAugust 21, October 21
  • CFebruary 20, October 21
  • DFebruary 20, April 21
  • EApril 21, August 21


Molly and her friends got on a Ferris wheel. When they entered the cabin at 3:15 pm, they were 5 m above the ground. The height of the cabin minutes after they got into it is given by . When were they 40 m above the ground? Give your answer to the nearest minute.

  • A3:28 pm, 3:32 pm
  • B3:27 pm, 3:33 pm
  • C3:23 pm, 3:27 pm
  • D3:23 pm, 3:17 pm
  • E3:17 pm, 3:33 pm