Editing Trigonometric functions (section)

== Notation ==
Conventionally, an abbreviation of each trigonometric function's name is used as its symbol in formulas. Today, the most common versions of these abbreviations are "{{math|sin}}" for sine, "{{math|cos}}" for cosine, "{{math|tan}}" or "{{math|tg}}" for tangent, "{{math|sec}}" for secant, "{{math|csc}}" or "{{math|cosec}}" for cosecant, and "{{math|cot}}" or "{{math|ctg}}" for cotangent. Historically, these abbreviations were first used in prose sentences to indicate particular [[line segment]]s or their lengths related to an [[circular arc|arc]] of an arbitrary circle, and later to indicate ratios of lengths, but as the [[history of the function concept|function concept developed]] in the 17th–18th century, they began to be considered as functions of real-number-valued angle measures, and written with [[functional notation]], for example {{math|sin(''x'')}}. Parentheses are still often omitted to reduce clutter, but are sometimes necessary; for example the expression <math>\sin x+y</math> would typically be interpreted to mean <math>(\sin x)+y,</math> so parentheses are required to express <math>\sin (x+y).</math>

A [[positive integer]] appearing as a superscript after the symbol of the function denotes [[exponentiation]], not [[Function composition#Functional powers|function composition]]. For example <math>\sin^2 x</math> and <math>\sin^2 (x)</math> denote <math>(\sin x)^2,</math> not <math>\sin(\sin x).</math> This differs from the (historically later) general functional notation in which <math>f^2(x) = (f \circ f)(x) = f(f(x)).</math>

In contrast, the superscript <math>-1</math> is commonly used to denote the [[inverse function]], not the [[multiplicative inverse |reciprocal]]. For example <math>\sin^{-1}x</math> and <math>\sin^{-1}(x)</math> denote the [[inverse trigonometric function]] alternatively written <math>\arcsin x\,.</math> The equation <math>\theta = \sin^{-1}x</math> implies <math>\sin \theta = x,</math> not <math>\theta \cdot \sin x = 1.</math> In this case, the superscript ''could'' be considered as denoting a composed or [[iterated function]], but negative superscripts other than <math>{-1}</math> are not in common use.