combine/trig - Maple Programming Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Mathematics : Basic Mathematics : Exponential, Trig, and Hyperbolic Functions : Manipulation : combine/trig

combine/trig

combine trigonometric terms

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

combine(f, trig);

Parameters

f

-

any expression

Description

• 

Products and powers of trigonometric terms involving sin, cos, sinh and cosh are combined into a sum of trigonometric terms by repeated application of the transformations

sinasinb12cosab12cosa+b

sinacosb12sinab+12sina+b

cosacosb12cosab+12cosa+b

• 

where  sina2  and  cosb2  are special cases of the above. The form of the result is a sum of trigonometric terms whose arguments are integral linear combinations of the original arguments.

• 

An important special case is when the input is a polynomial in sinx and cosx over a field, in which case the result is a canonical form; namely,

i=nnaisinix+i=nnbicosix

• 

where ai, bi are in the field and n is bounded by the total degree of the input polynomial in sinx and cosx.

Examples

combinesinx2,trig

1212cos2x

(1)

combinesinhxcoshx,trig

12sinh2x

(2)

combine2sinxcosy,trig

sinx+y+sinxy

(3)

fsinx2cosx+3cosx3+2sinxcosx

f:=sinx2cosx+3cosx3+2sinxcosx

(4)

combinef,trig

52cosx+12cos3x+sin2x

(5)

f512sinx5cosx5

f:=512sinx5cosx5

(6)

combinef,trig

sin10x+10sin2x5sin6x

(7)

Download Help Document

Was this information helpful?



Please add your Comment (Optional)
E-mail Address (Optional)
What is ? This question helps us to combat spam