Trigonometric Functions – A guide for teachers

ASSUMED KNOWLEDGE

• Familiarity with the material in the modules, Introduction to Trigonometry and Further Trigonometry.
• Knowledge of basic coordinate geometry.
• Introductory graphs and functions.
• Facility with simple algebra, formulas and equations.

MOTIVATION

In the module, Further Trigonometry, we saw how to use points on the unit circle to extend the definition of the trigonometric ratios to include obtuse angles. That same construction can be extended to angles between 180° and 360° and beyond. The sine, cosine and tangent of negative angles can be defined as well. Once we can find the sine, cosine and tangent of any angle, we can use a table of values to plot the graphs of the functions y = sin x, y = cos x and y = tan x. In this module, we will deal only with the graphs of the first two functions. The graphs of the sine and cosine functions are used to model wave motion and form the basis for applications ranging from tidal movement to signal processing which is fundamental in modern telecommunications and radio-astronomy. This provides a breathtaking example of how a simple idea involving geometry and ratio was abstracted and developed into a remarkably powerful tool that has changed the world.

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