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Egwald Mathematics: Hyperbolic Functions
by
Elmer G. Wiens
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Hyperbolic Functions
The hyperbolic functions are very useful in solving many engineering problems. While their names resemble the natural trigonometric functions, they are not periodic like the trig. functions. The hyperbolic functions are based on the exponential function, which is definitely not periodic.
| hyperbolic cosine: | cosh(u) = .5 * (eu + e-u) |
hyperbolic sine: | sinh(u) = .5 * (eu - e-u) |
| hyperbolic tangent: | tanh(u) = sinh(u) / cosh(u) |
hyperbolic cotangent: | coth(u) = cosh(u) / sinh(u) |
| hyperbolic secant: | sech(u) = 1 / cosh(u) |
hyperbolic cosecant: | csch(u) = 1 / sinh(u) |
As u goes from -infinity to +infinity, the point (x, y) = (cosh(u),sinh(u)) traces out the unit hyperbola:
x^2 - y^2 = 1
as, cosh2(u) - sinh2(u) = 1
| y = ex | x = cosh(u), y = sinh(u) |
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