Research-based guidance and classroom activities for teachers of mathematics

Trigonometric functions

Trigonometric functions are pervasive in many parts of pure and applied mathematics. Students learn about trigonometric functions, trigonometric equations and trigonometric identities. Beyond this there is the use of complex numbers in trigonometric expressions and in, for example, Euler’s formula.

Challenges for students

In preparation for learning about trigonometric functions, students need to be familiar with a range of ideas across algebra and geometry. Trigonometry may be the first context in which students meet functions that are not polynomials in x and that are represented using a name, as well as the first context in which the notion of inverse function has to be discussed in depth.

For these reasons, the initial stages of learning about trigonometric functions can be challenging for students. This is partly because of the need to relate diagrams of triangles to numerical relationships and then manipulate the symbols involved; and partly because students have trouble viewing trigonometric relationships as functions, particularly if most of their previous experience has been using formulae to solve right-angled triangles.

Teaching approaches

There are different approaches to teaching about trigonometric functions; some emphasise multiplicative relationships, while others emphasise spatial meaning. Such approaches aim to give experience of what the trigonometric functions (such as ‘sine’) are, and what they do.