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
open all close allScope (4)
Hyperbolic trigonometric expressions:
TrigReduce threads over lists:
TrigReduce threads over equations, inequalities and logical operations:
Options (1)
Applications (1)
Find the period of a trigonometric polynomial:
FunctionPeriod gives a multiple of the minimal period:
Reducing the expression helps to find the minimal period:
Periodicity can also be observed from the plots of the original function and the shifted function:
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)
Text
Wolfram Research (1996), TrigReduce, Wolfram Language function, https://reference.wolfram.com/language/ref/TrigReduce.html (updated 2007).
CMS
Wolfram Language. 1996. "TrigReduce." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2007. https://reference.wolfram.com/language/ref/TrigReduce.html.
APA
Wolfram Language. (1996). TrigReduce. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/TrigReduce.html