What is function $\sin$ without $x$? I'm solving a problem set in ODE:

This is the first time in my life that I see such functions $\sin,\cos,\tan$ without argument $x$.
I would like to ask if $\sin,\cos,\tan$ mean $\sin x,\cos x,\tan x$ or they mean something else.
Thank you so much!

In this context you are dealing with functions $\mathbb R\to\mathbb R$.


*

*$x$ stands for the identity function.

*$y$ stands for some function.

*$y'$ stands for the derivative of function $y$.

*$\sin$ stands for the function prescribed by $z\mapsto\sin(z)$ (same story for $\cos$ and $\tan$).


But I must say that there is some inconsistency which causes confusion. 


*

*The author sometimes uses $y$ and another time $y(x)$. 

*If $x$ is used as a function then IMV it is better to use another symbol (e.g. $z$) as argument of the function. Another way is not writing $x$ but writing $\mathsf{id}$ so that $x$ can be reserved as argument (as we are used to).

