What is the order of operations in trig functions? Is $\sin(x)^2$ the same as $\sin^2(x)$ or $\sin(x^2)$? I thought it would mean the former interpretation, $\sin^2(x)$, rather than the latter, but my teacher and I had a long argument on this and in the end I found that Casio calculators have a space between before the parenthesis, so it would look like $\sin\text{ }(x)^2$ and what the calculator would do is calculate $x^2$, and then take the $\sin$ of that whereas on Texas calculators, there is no space, so it would look like $\sin(x)^2$ and it will calculate $\sin$ of $x$ first, and then take the result and square it.
$$\Large \sin(x)^2 \equiv [\sin(x)]^2 \equiv \sin^2(x).$$

Think about it: if $\sin(x)^2$ were equivalent to $\sin(x^2),$ then the exponent $\quad ^2 \quad$ would be inside the brackets.
It is not only in trigonometric functions, all functions fall under this notation. $$(f(x))^2 \equiv f(x)^2 \equiv f^2(x)$$
It is commonly used for trigonometric functions and logarithmic ones, but it doesn't mean it is wrong for the rest of functions.