Math Shorts - Integrals II by Metin Bektas

Author:Metin Bektas [Bektas, Metin]
Language: eng
Format: azw3
Published: 2014-08-19T00:00:00+00:00

Special values worth keeping in mind are: sinh(0) = tanh(0) = 0 and cosh(0) = 1 (these are easy to remember since the same holds true for their non-hyperbolic brothers and sisters). The hyperbolic tangent approaches 1 for x → ∞ and -1 for x → -∞. The hyperbolic counterpart to the identity sin2(x) + cos2(x) = 1 is the relation:

The proof is simple and straight-forward:

Note that I used ex·e-x = 1. Another side note: there's a really cool way of transforming any trigonometric identity into a hyperbolic identity. Just replace sin(x) with i·sinh(x), the letter i stands for the imaginary unit, and cos(x) with cosh(x). Keep in mind that i2 = -1 and you're done.

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