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Inverse Hyperbolic Functions

★★★★☆Undergraduate

📖Definition

Inverse functions of hyperbolic functions, expressible in terms of logarithms.

📐Formulas

arsinh x = ln(x + √x² + 1)

Inverse hyperbolic sine

arcosh x = ln(x + √x² - 1) (x ≥ 1)

Inverse hyperbolic cosine

artanh x = (1)/(2)ln(1+x)/(1-x) (|x| < 1)

Inverse hyperbolic tangent

✏️Examples

예제 1★★☆☆☆

Find arsinh(0).

예제 2★★☆☆☆

Find arcosh(1).

Applications

Integration

Expressing certain integral results

Physics

Relativistic velocity addition

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Applications

#역쌍곡선함수#arsinh#arcosh#artanh#inverse hyperbolic