Sine is a function and functions are all written as $f(x)$ where $f$ is the 'name' of the function. We never see any textbook using $f\ x$ to denote a function of $x$.
And also, using $\sin(x)$ saves us from blunders like $\sin x^2$ which can be interpreted as either $\sin(x^2)$ or $\sin(x)^2$. Even writing $\sin(x)^2$ as $\sin^2 x$, is not a very good notation because, $f^2(x)$ generally means $f\circ f(x)$. And $\sin^2 x$ can be interpreted as $\sin(\sin(x))$ which is not equal to $\sin(x)^2$. This contributes to things like $\sin^{-1} x$, which I think doesn't make any sense. I mean, what does $\sin^{-1}x$ supposed to mean? If $\sin^2 x$ is $(\sin x)^2$, then, $$\sin^{-1}x=(\sin x)^{-1}=\frac{1}{\sin x}\qquad\text{or}\qquad\sin^{-1}x=\frac{1}{\sin}(x)$$ $\displaystyle\frac{1}{\sin}(x)$ feels so strange. But $\sin^{-1} x$ is supposed to mean $\arcsin(x)$. Same things happen with all trigonometric functions. Shouldn't $\sin x$ be inaccurate way of denoting $\sin(x)$? Then why many, many books write $\sin(x)$ as $\sin x$? Isn't it plain wrong?