Powers of trigonometric functions
From Why start at x, y, z
When writing a power of a trigonometric function, it's common to write the power as a superscript before the brackets:
\[ \sin^2(x) = (\sin(x))^2 \]
This conflicts with the conventional notation for inverses and repeated application of functions:
\[ f^2(x) = f(f(x)) \]
\[ y = f^{-1}(x) \implies x = f(y) \]
In his entry on Notation in the Edinburgh Encyclopedia [1], Charles Babbage is scathing about this convention.
Although a definition can not be false, it may be improper.
- ↑ The Edinburgh Encyclopedia, 1830, pp. 398-399. Copy on HathiTrust
