Editing Inverse function (section)

===Trigonometric inverses===
[[Image:Gràfica del arcsinus.png|right|thumb|The [[arcsine]] is a partial inverse of the [[sine]] function.]]

The above considerations are particularly important for defining the inverses of [[trigonometric functions]]. For example, the [[sine function]] is not one-to-one, since

: <math>\sin(x + 2\pi) = \sin(x)</math>

for every real {{mvar|x}} (and more generally {{math|1= sin(''x'' + 2{{pi}}''n'') = sin(''x'')}} for every [[integer]] {{mvar|n}}). However, the sine is one-to-one on the interval
{{closed-closed|−{{sfrac|{{pi}}|2}}, {{sfrac|{{pi}}|2}}}}, and the corresponding partial inverse is called the [[arcsine]]. This is considered the principal branch of the inverse sine, so the principal value of the inverse sine is always between −{{sfrac|{{pi}}|2}} and {{sfrac|{{pi}}|2}}. The following table describes the principal branch of each inverse trigonometric function:<ref>{{harvnb|Briggs|Cochran|2011|loc=pp. 39–42}}</ref>
{| class="wikitable" style="text-align:center"
|-
!function
!Range of usual [[principal value]]
|-
| arcsin || {{math|−{{sfrac|{{pi}}|2}} ≤ sin<sup>−1</sup>(''x'') ≤ {{sfrac|{{pi}}|2}}}}
|-
| arccos || {{math|0 ≤ cos<sup>−1</sup>(''x'') ≤ {{pi}}}}
|-
| arctan || {{math|−{{sfrac|π|2}} < tan<sup>−1</sup>(''x'') < {{sfrac|{{pi}}|2}}}}
|-
| arccot || {{math|0 < cot<sup>−1</sup>(''x'') < {{pi}}}}
|-
| arcsec || {{math|0 ≤ sec<sup>−1</sup>(''x'') ≤ {{pi}}}}
|-
| arccsc || {{math|−{{sfrac|{{pi}}|2}} ≤ csc<sup>−1</sup>(''x'') ≤ {{sfrac|{{pi}}|2}}}}
|-
|}