# Simplifying and expressing preferentially with sines: trigsin

### 5.23.23 Simplifying and expressing preferentially with sines: trigsin

Any trigonometric function can be written in terms of sins and coss, and with the identity sin(x)2+cos(x)2=1, the even powers of cos can be turned into powers of sin. The trigsin command performs these substitutions.

- trigsin takes one argument:
  expr, an expression containing trigonometric functions.
- trigsin(expr) returns expr with the trigonometric functions rewritten in terms of sin and cos, with as many coss as possible transformed to sins.

#### Example.

Input:

trigsin(sin(x)^4+cos(x)^2+1)

Output:

sin4x−sin2x+2