TrigReduce

TrigReduce[expr]

rewrites products and powers of trigonometric functions in expr in terms of trigonometric functions with combined arguments.

Details and Options

  • TrigReduce operates on both circular and hyperbolic functions.
  • Given a trigonometric polynomial, TrigReduce typically yields a linear expression involving trigonometric functions with more complicated arguments.
  • TrigReduce automatically threads over lists, as well as equations, inequalities and logic functions.

Examples

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Basic Examples  (1)

Scope  (1)

TrigReduce operates on hyperbolic trigonometric functions:

Options  (1)

Modulus  (1)

Manipulation with polynomials is performed using modular arithmetic:

Compare with the reduction over rationals:

Applications  (1)

Find the period of a trigonometric polynomial:

Verification:

Properties & Relations  (3)

ChebyshevT[n,Cos[x]] reduces to Cos[n x]:

ChebyshevU[n,Cos[x]] is related to Sin[n x]:

TrigReduce and TrigExpand are, generically, inverses of each other:

TrigReduce threads over lists, inequalities, equations and logical operations:

Possible Issues  (3)

The value of the option Modulus must be an integer:

TrigReduce requires explicit trigonometric functions:

Use ExpToTrig to convert exponential to trigonometric functions:

Reducing constants might not always give the desired effect:

Neat Examples  (1)

Introduced in 1996
 (3.0)
 |
Updated in 2007
 (6.0)