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 used by many sailors. They 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 using the rule of twelfths to actual values of the sine of various angles.