Editing Trigonometric functions (section)

==Inverse functions==
{{Main|Inverse trigonometric functions}}
The trigonometric functions are periodic, and hence not [[injective function|injective]], so strictly speaking, they do not have an [[inverse function]]. However, on each interval on which a trigonometric function is [[monotonic]], one can define an inverse function, and this defines inverse trigonometric functions as [[multivalued function]]s. To define a true inverse function, one must restrict the domain to an interval where the function is monotonic, and is thus [[bijection|bijective]] from this interval to its image by the function. The common choice for this interval, called the set of [[principal value]]s, is given in the following table. As usual, the inverse trigonometric functions are denoted with the prefix "arc" before the name or its abbreviation of the function.
{| class="wikitable" style="text-align: center;"
! Function !! Definition !! Domain !! Set of principal values
|-
| <math>y = \arcsin x</math> || <math>\sin y = x</math> || <math>-1 \le x \le 1</math> || <math display="inline">-\frac{\pi}{2} \le y \le \frac{\pi}{2}</math>
|-
| <math>y = \arccos x</math> || <math>\cos y = x</math> || <math>-1 \le x \le 1</math> || <math display="inline">0 \le y \le \pi</math>
|-
| <math>y = \arctan x</math> || <math>\tan y = x</math> || <math>-\infty < x < \infty</math> || <math display="inline">-\frac{\pi}{2} < y < \frac{\pi}{2}</math>
|-
| <math>y = \arccot x</math> || <math>\cot y = x</math> || <math>-\infty < x < \infty</math> || <math display="inline">0 < y < \pi</math>
|- 
| <math>y = \arcsec x</math> || <math>\sec y = x</math> || <math>x<-1 \text{ or } x>1</math> || <math display="inline">0 \le y \le \pi,\; y \ne \frac{\pi}{2}</math>
|-
| <math>y = \arccsc x</math> || <math>\csc y = x</math> || <math>x<-1 \text{ or } x>1</math> || <math display="inline">-\frac{\pi}{2} \le y \le \frac{\pi}{2},\; y \ne 0</math>
|}

The notations {{math|sin<sup>−1</sup>}}, {{math|cos<sup>−1</sup>}}, etc. are often used for {{math|arcsin}} and {{math|arccos}}, etc. When this notation is used, inverse functions could be confused with multiplicative inverses. The notation with the "arc" prefix avoids such a confusion, though "arcsec" for arcsecant can be confused with "[[arcsecond]]".

Just like the sine and cosine, the inverse trigonometric functions can also be expressed in terms of infinite series. They can also be expressed in terms of [[complex logarithm]]s.