Operators and Spacing in LaTeX Math

\sin x, \cos x, \log x, \exp x, \lim_{n\to\infty} a_n
\operatorname{Var}(X)
\DeclareMathOperator{\argmax}{arg\,max}

a\,b \quad a\qquad b \; c \! d

\text{if } x > 0, \text{ then } f(x)=x^2.