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### Trigonometry

Let  us now consider some trigonometric expressions. For example:

When you type this expression into Maxima, Maple or Mathematica, you must remember that is really a shorthand for . So let us try to obtain the above result in Maxima first:

The function trigexpand
works on expressions such as and . In turn function trigsimp employs the identities and to simplify expressions containing , , etc. to , , , . Further simplification, if needed, may be obtained by using function trigreduce on the result.2.4

In Maple we don't have to muck around with specialised functions for trigonometry. Maple has a general purpose wrapper called simplify, which recognises the nature of the expression and applies appropriate rules until the result is as compact and simple as possible:

Mathematica will do something quite different here with its own version of Simplify:

We can use Maxima in order to check that

Function trigrat
gives a canonical  simplified quasilinear form of a trigonometrical expression.2.5

Mathematica also has similar functions, called TrigExpand, TrigFactor, and TrigReduce, but its TrigExpand doesn't work the same way as in Maxima:

Next: Fractions Up: Algebra Previous: Polynomials
Zdzislaw Meglicki
2001-02-26