Hyperbolic Functions Calculator (sinh, cosh, tanh)
Welcome to the Hyperbolic Functions Calculator. This tool is designed for students, engineers, and math enthusiasts to compute the hyperbolic sine (sinh), cosine (cosh), and tangent (tanh) of a given value. Whether you're tackling complex mathematics or engineering projects, this calculator provides precise and quick results.
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Source of Data and Methodology
Calculations are based on standard mathematical formulas for hyperbolic functions. For further reading, refer to "Mathematical Functions: Handbook of Definitions, Formulas, and Graphs" by the Mathematical Association.
Tutti i calcoli si basano rigorosamente sulle formule e sui dati forniti da questa fonte.
The Formula Explained
sinh(x): \( \mathrm{sinh}(x) = \frac{e^x - e^{-x}}{2} \)
cosh(x): \( \mathrm{cosh}(x) = \frac{e^x + e^{-x}}{2} \)
tanh(x): \( \mathrm{tanh}(x) = \frac{\mathrm{sinh}(x)}{\mathrm{cosh}(x)} \)
Glossary of Variables
- x: The input value for which the hyperbolic functions are calculated.
- sinh(x): Hyperbolic sine of x.
- cosh(x): Hyperbolic cosine of x.
- tanh(x): Hyperbolic tangent of x.
How It Works: A Step-by-Step Example
For an input value of 1, the calculator computes the following:
- sinh(1): \( \frac{e^1 - e^{-1}}{2} \approx 1.175 \)
- cosh(1): \( \frac{e^1 + e^{-1}}{2} \approx 1.543 \)
- tanh(1): \( \frac{\mathrm{sinh}(1)}{\mathrm{cosh}(1)} \approx 0.761 \)
Frequently Asked Questions (FAQ)
What are hyperbolic functions used for?
Hyperbolic functions are used in various fields such as engineering, physics, and mathematics for modeling hyperbolic structures, waveforms, and more.
How do hyperbolic functions differ from trigonometric functions?
While trigonometric functions are based on the unit circle, hyperbolic functions are based on the hyperbola, leading to different properties and applications.
Can I calculate inverse hyperbolic functions with this calculator?
This calculator currently focuses on sinh, cosh, and tanh. Inverse functions may be supported in future updates.
What is the range of values for sinh, cosh, and tanh?
The range of sinh and tanh is all real numbers, while cosh is always greater than or equal to 1.
Are hyperbolic functions periodic?
Unlike trigonometric functions, hyperbolic functions are not periodic.