Definitions
from Wiktionary, Creative Commons Attribution/Share-Alike License.
- abbreviation mathematics The area hyberbolic cotangent function, i.e., the inverse hyperbolic cotangent function.
Etymologies
from Wiktionary, Creative Commons Attribution/Share-Alike License
arc- + coth
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Examples
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In for - mulas and equations, they are abbreviated arcsinh or sinhÀ1, arccosh or coshÀ1, arctanh or tanhÀ1, arccsch or cschÀ1, arcsech or sechÀ1, and arccoth or cothÀ1 respectively.
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CHAPTER 4 Hyperbolic Functions 65 arcsinh x ¼ ln ½x þ ðx2 þ 1Þ1 = 2 Š arccosh x ¼ ln ½x þ ðx2 À 1Þ1 = 2 Š arctanh x ¼ 0: 5 ln ½ð1 þ xÞ = ð1 À xÞŠ arccsch x ¼ ln ½xÀ1 þ ðxÀ2 þ 1Þ1 = 2 Š arcsech x ¼ ln ½xÀ1 þ ðxÀ2 À 1Þ1 = 2 Š arccoth x ¼ 0: 5 ln ½ðx þ 1Þ = ðx À 1ÞŠ In these expressions, the values 0.5 represent exactly 1 = 2.
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