Hyperbolic Functions Calculator
Use our hyperbolic functions calculator to compute sinh(x), cosh(x), tanh(x), coth(x), sech(x), and csch(x). Includes what are hyperbolic functions, how to calculate hyperbolic functions, key hyperbolic functions rules, and tips for finding hyperbolic functions on a calculator (Calc BC and calculus use cases).
What are Hyperbolic Functions?
Hyperbolic functions are a family of functions similar in style to trigonometric functions, but based on the geometry of a hyperbola instead of a circle. The main hyperbolic functions are sinh, cosh, and tanh.
If you’re asking what are hyperbolic functions used for or what is the point of hyperbolic functions, they appear in hyperbolic function calculus, differential equations, physics (like catenary curves and relativity), and engineering models involving growth/decay and wave behavior.
Many students ask are hyperbolic functions in Calc BC—yes, they commonly show up in calculus topics like derivatives, integrals, and solving certain differential equations.
Hyperbolic Functions Rules and Formulas
Hyperbolic functions can be defined using exponentials. This hyperbolic calculator with steps shows the standard definitions and key identities.
Defined for all real x.
Defined for all real x.
Defined for all real x (cosh(x) is never 0).
Undefined at x = 0 because sinh(0)=0.
Defined for all real x.
Undefined at x = 0 because sinh(0)=0.
This identity is the hyperbolic analog of trig identities and is central in hyperbolic function calculus.
And because sinh(0)=0, csch(0) and coth(0) are undefined.
How to Use the Hyperbolic Functions Calculator
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Enter your value for x.
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The calculator computes sinh(x), cosh(x), tanh(x), coth(x), sech(x), and csch(x).
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Use the results for calculus, algebra, or engineering problems involving hyperbolic function rules and identities.
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If you need hyperbolic functions on calculator hardware, look for sinh, cosh, tanh (often under a SHIFT/2nd function menu).
Frequently Asked Questions
Hyperbolic functions are functions like sinh, cosh, and tanh defined using exponentials and related to hyperbola geometry.
You can use the exponential definitions: sinh(x)=(e^x−e^-x)/2, cosh(x)=(e^x+e^-x)/2, and tanh(x)=sinh(x)/cosh(x).
Many scientific calculators include sinh, cosh, tanh directly or under SHIFT/2nd. If not, use the exponential definitions with e^x.
Yes, they commonly appear in calculus topics like derivatives, integrals, and differential equations, depending on the curriculum.
They’re used in calculus, differential equations, physics (catenary curves, relativity), and engineering models.
They provide natural tools for modeling hyperbolic geometry and solutions to many real-world systems, especially those involving exponential behavior.
They simplify many calculus and physics problems and have clean identities like cosh^2(x) − sinh^2(x) = 1.
Common rules include identities like cosh^2(x) − sinh^2(x) = 1 and relationships like tanh(x)=sinh(x)/cosh(x), plus standard derivative/integral rules in calculus.
Yes—the page includes the defining formulas and identities used to compute each hyperbolic function.
Because sinh(0)=0 and both coth(x)=cosh(x)/sinh(x) and csch(x)=1/sinh(x) would divide by 0.