Trigonometry: Rule of Twelfths

Australian curriculum number (ACMMG274)

Students learn that tidal patterns closely match a sine curve and use a well-known rule of thumb to approximate tidal heights. They develop a deeper understanding and appreciation of the properties of the sine curve and its real-life occurrences.

This sequence is for students who:

  • are familiar with the unit circle and have examined how the vertical distance from the circle to the x-axis varies to plot a sine curve.
  • understand that the sine of an angle can be evaluated for angles greater than 90°.


Lesson 1: Rule of Twelfths

Students learn about the rule of twelfths: a practical way to calculate tidal heights that is used by many sailors. Students apply the rule to graph tidal heights and observe that the graph resembles a sinusoidal curve. They extend their knowledge by comparing the results obtained from using the rule of twelfths with the actual values of the sine of various angles.


Last updated June 26 2020.