Hyperbolic function (English)
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Definition (advanced level)
A group of functions related to the trigonometric functions:
hyperbolic sin of x is written sinh(x) (pronounced 'shine x')
hyperbolic cos of x is written cosh(x) ('cosh x')
hyperbolic tan of x is written tanh(x) ('tansh x')
Definitions; sinh(x) = [exp(x) - exp(-x)]/2
cosh(x) = [exp(x) + exp(-x)]/2
tanh(x) = sinh(x)/cosh(x)
There are also sech, coth and cosech, defined as 1/cosh, 1/sinh and 1/tanh respectively.
hyperbolic sin of x is written sinh(x) (pronounced 'shine x')
hyperbolic cos of x is written cosh(x) ('cosh x')
hyperbolic tan of x is written tanh(x) ('tansh x')
Definitions; sinh(x) = [exp(x) - exp(-x)]/2
cosh(x) = [exp(x) + exp(-x)]/2
tanh(x) = sinh(x)/cosh(x)
There are also sech, coth and cosech, defined as 1/cosh, 1/sinh and 1/tanh respectively.
Relations
- broader:
- (en) Function
- narrower:
- (en) Hyperbolic cosecant
- (en) Hyperbolic cosine
- (en) Hyperbolic cotangent
- (en) Hyperbolic coversine
- (en) Hyperbolic haversine
- (en) Hyperbolic secant
- (en) Hyperbolic sine
- (en) Hyperbolic tangent
- (en) Hyperbolic versine
- (en) Inverse hyperbolic function
- references:
- (en) Trigonometric function
- referenced:
- (en) Hyperbolic derivative
- (en) Hyperbolic double-angle formula
- (en) Hyperbolic identity
- (en) Hyperbolic integral
- (en) Hyperbolic power series
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