A New Toolkit for Simplifying Trigonometric Expressions

Xiuqin Zhong
Chengdu Institute of Computer Applications
Chinese Academy of Sciences
Chengdu 610041, China

Abstract. Simplification of trigonometric expressions is an important problem that has not been completely solved by current computer algebraic systems. This paper presents a new method for simplifying trigonometric expressions. The method is based on a number of unique prescriptions for the ordering of some trigonometric rules, which have been derived by observing how human experts follow their intuitive rules, and it can conveniently simplify trigonometric expressions automatically or interactively. We have implemented the procedure in Lisp because of its suitability for formula manipulations and rule-based reasoning systems. Consequently it can achieve much better results than Maple and Mathematica in the simplification of many trigonometric expressions, and it can generate readable proofs that can be verified step by step. Therefore, the toolkit is helpful in K12 education.