Trigonometry - modelling with trigonometric functions

The London Eye (the world's largest Ferris wheel) has a diameter of 135 metres and completes one revolution in 30 minutes.

Ferris wheel demonstration
Observe the Ferris wheel from different viewpoints. Focus on the vertical motion.

If you go for a ride on the wheel, how high are you after 6 minutes and when are you 50 metres above the ground? Use a trigonometric function to create a model and answer these questions - solution.

At any place on the earth, the amount of daylight varies during the year.

Choose some different places and find the amount of daylight in minutes on several days spread throughout the year. For each place, use a trigonometric function to model how the amount of daylight varies with the day of the year.

• Do the functions for different places have the same period of 365 days?
• How does latitude effect the amplitude of the function?
• At what days during the year, do all places on earth have the same amount of daylight (equinox)? Do your functions suggest that this amount is 12 hours (720 minutes)? Why might you expect a value slightly larger than 720 minutes?
• Data and calculations for Brisbane, Adelaide and London for 1999.

Investigate a trigonometric model for temperature data.

• Monthly averages are available from http://www.worldclimate.com/worldclimate/.
• Average monthly minimum and maximum temperatures for Brisbane, Adelaide and New York.
• Solutions for Brisbane, Adelaide and New York.

These questions (about tides, a pendulum and combining trigonometric functions) have been prepared by Peter Cazalet (Collie Senior High School). Solutions are provided.

Using suitable trigonometric functions:

• Collection of problems
• Answers

The use of trigonometric functions to predict tide heights is dealt with in the paper:

•  http://www.math.sunysb.edu/~tony/tides/index.html