Reduction formulas

Reduction formulas are used to simplify trigonometric functions of argument of the form , for example:

General algorithm

General algorithm can be applied to of argument of the form :

1. Due to periodicity, ignore in case of and in case of :

2. If, in , , rewrite as

   for example:

3. Using the trig unit circle, define the sign () of the initial function: it will be the sign of the result

4. If, after step 2, the argument is of the form or , then the resulting function will be co-function of the initial function, in other words:

   If then the resulting function does not change, in other words:

Using argument shifts and periodicity

Trigonometric formulas can be successfully simplified without memorizing the above algorithm if the following principles are understood:

Redundancy due to periodicity

Since are periodic in and are periodic in ,

` tan, cot ` of ` alpha +- pi/2 `

` sin, cos ` of ` alpha +- pi `

` sin, cos ` of ` alpha +- pi/2 `