Trivia: Question about arranging terms

[DrD]

If there is a lexicon formality, how should equal power terms involving cos() and sin() be displayed in "proper" order?

Here's an example:

y:=cos(x^4)^2;
y'; ==> -2*4*x^3*sin(x^4)*cos(x^4) Notice the factoring order
collect(y'); ==> -8*x^3*cos(x^4)*sin(x^4) The cos() and sin() get reversed here.

(In this case increasing power order): Without any mathematical difference, what, if any, is the proper, or most formal way to express the ordering of the trig terms?

[salvomic]

(In this case increasing power order): Without any mathematical difference, what, if any, is the proper, or most formal way to express the ordering of the trig terms?
[/quote]

In the old Italian books of trigonometry we have: SIN, COS, TAN and decreasing power order (x^4, x^3, x^2..., about my math professor), but if (generally) COS in x and SIN is y, we should have COS, SIN, TAN, I think...