In this Unit we deal with trigonometric identities. These identities are particularly useful in doing the algebra of trigonometry. In this application of the identities complex expressions are simplified and converted into different equivalent forms. This algebraic nature of trigonometry is taught at secondary school level, not only as a stepping stone towards further tertiary studies, which may require some form of trigonometry knowledge, but also as a tool to develop learners’ logical reasoning.
Often learners don't know how to start to prove an identity without any hint, even if they know every trigonometric formula. In this unit we will explore some general ideas to prove an identity, and in doing so provide an opportunity for you to pass this on to your learners, in order to improve their mathematics problem solving skills.
The usual approach to identities is the memorisation of the basic identities with little or no reference to the graphical meaning of the identities. The learners are then expected to be able to substitute and manipulate to prove given more complex identities. In this module we will try to give some graphical interpretation of the use of identities.