triangularize SciMax Toolbox trigexpandplus

SciMax Toolbox >> trigexpand

trigexpand

Maxima Function

Calling Sequence

trigexpand (expr)

Description

Expands trigonometric and hyperbolic functions of sums of angles and of multiple angles occurring in expr. For best results, expr should be expanded. To enhance user control of simplification, this function expands only one level at a time, expanding sums of angles or multiple angles. To obtain full expansion into sines and cosines immediately, set the switch trigexpand: true.

trigexpand is governed by the following global flags:

trigexpand

If true causes expansion of all expressions containing sin's and cos's occurring subsequently.

halfangles

If true causes half-angles to be simplified away.

trigexpandplus

Controls the "sum" rule for trigexpand, expansion of sums (e.g. sin(x + y)) will take place only if trigexpandplus is true.

trigexpandtimes

Controls the "product" rule for trigexpand, expansion of products (e.g. sin(2 x)) will take place only if trigexpandtimes is true.

Examples:

(%i1) x+sin(3*x)/sin(x),trigexpand=true,expand;
                         2           2
(%o1)               - sin (x) + 3 cos (x) + x
(%i2) trigexpand(sin(10*x+y));
(%o2)          cos(10 x) sin(y) + sin(10 x) cos(y)
triangularize SciMax Toolbox trigexpandplus