arcsech

HYPERBOLIC ARCSECANT Figure 4-11 is a graph of the function y ¼ arcsech x (or y ¼ sechÀ1 x).

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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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A simpler way to express e to the power of arcsech x is (a) non-existent because such an expression is too complicated to deal with (b) xÀ1 þ (x-2 - 1) 1/2 (c) xÀ1 þ (x-2 þ 1) 1/2 (d) xÀ1 - (x-2 - 1) 1/2 8.

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