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July 7, 2022


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Trigonometric functions for high school level, a PDF guide course by mathcentre.ac.uk.

The sine, cosine and tangent of an angle are all defined in terms of trigonometry, but they can also be expressed as functions. In this unit we examine these functions and their graphs. We also see how to restrict the domain of each function in order to define an inverse function.

In order to master the techniques explained here it is vital that you undertake plenty of practice exercises so that they become second nature.

After reading this text, and/or viewing the video tutorial on this topic, you should be able to:

  • specify the domain and the range of the three trigonometric functions f(x) = sin x, f(x) = cos x and f(x) = tan x,
  • understand the difference between each function expressed in degrees and the corresponding function expressed in radians,
  • express the periodicity of each function in either degrees or radians,
  • specify a suitable restriction for the domain of each function so that an inverse function can be defined,
  • find the appropriate value of x (in either degrees or radians) when given a value of sin x, cos x or tan x.


  • Introduction
  • The sine function f(x) = sin x
  • The cosine function f(x) = cos x
  • The tangent function f(x) = tan x

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