Introduction to Hyperbolic Function Calculator:
Hyperbolic function calculator is an online tool used to find the hyperbolic function identities for exponential functions of the given x value.
The hyperbolic functions calculator helps you to determine the hyperbolic function of the exponential function and its inverse in all six identities of hyperbolic functions in less than a minute.
What is Hyperbolic Functions?
Hyperbolic function is the cognate function to the trigonometry function but the hyperbolic function is not present in a circle.
Although the hyperbolic functions have six identities trigonometry functions have like sinh, cosh,tanh, sech,cosech, coth, etc. Hyperbolic function coordinates form in the right equilateral hyperbola as a coshθ, sinhθ, etc.
Rules Followed by Hyperbolic Functions Calculator:
There are six identities of algebraic expressions where exponential functions are used to solve different kinds of problems in mathematics. Our Hyperbolic function calculator follows the following rule to solve the problems.
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Sinh
Sinh is the odd part of the algebraic function where e (Euler constant ) is used as an exponential function and its inverse is present.
$$ sinh \; x \;=\; \frac{e^x - e^{-x}}{2} $$
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Cosh
Cosh is the even part of the algebraic function where the exponential function and its inverse are present.
$$ cosh \; x \;=\; \frac{e^x + e^{-x}}{2} $$
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Tanh
Sinh is the odd part and cosh is the even part of the algebraic functions the hyperbolic function calculator divides it. where (Euler constant e is used) exponential function and its inverse are involved for tangent or tanh function.
$$ tanh (x) \;=\; \frac{sinh(x)}{cosh(x)} \;=\; \frac{(e^x - e^{-x})}{(e^x + e^{-x})} $$
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Sech
Sech is the odd part of the algebraic function and it is the inverse of cosh where (Euler constant e is used) exponential function and its inverse are present.
$$ sech (x) \;=\; \frac{1}{cosh(x)} \;=\; \frac{2}{e^x + e^{-x}} $$
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Cosech
Cosech is the odd part of the algebraic function and it is the inverse function ofSinh where (Euler constant e is used) exponential function and its inverse are present.
$$ csch(x) \;=\; \frac{1}{sinh(x)} \;=\; \frac{2}{e^x - e^{-x}} $$
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Coth
Coth is the odd part of the algebraic function, it is the inverse function of tanh where (Euler constant e is used) exponential function and its inverse are present.
$$ coth(x) \;=\; \frac{1}{tanh(x)} \;=\; \frac{(e^x + e^{-x})}{(e^x - e^{-x})} $$
Working Mechanism of Hyperbolic Calculator:
The hyperbolic trig calculator is an amazing tool for evaluating the trigonometry hyperbolic function using the simplest method. You can give various types of hyperbolic functions identities and this calculator will provide you solutions in steps.
When you add the input function in the hyperbolic tangent calculator, it analyzes the behavior of a function. After checking the nature of the function it will apply the formula of the hyperbolic function that is mentioned in the above heading.
Let's take the given example to elaborate on the working procedure of our hyperbolic cosine calculator, that is y=coshx. It applies the cosh(x) formula of the x exponential variable and then simplifies it. As you can see after simplification it becomes a quadratic equation.
The Hyperbolic function calculator applies the quadratic formula to solve the quadratic equation and gives the solution of y in a few seconds.
Hyperbolic Functions Identities - Examples
An example is given below to let you know about the manual calculation of solving hyperbolic function problems and to know how our hyperbolic calculator shows the results,
Example:
$$ Let \; y \;=\; cosh \; x. Solve\; for \; x: $$
Solution:
$$ y \;=\; \frac{e^x + e^{-x}}{2} $$
$$ 2y \;=\; e^x + e^{-x} $$
$$ 2ye^x \;=\; e^{2x} + 1 $$
$$ 0 \;=\; e^{2x} - 2ye^x + 1 $$
$$ e^x \;=\; \frac{2y \pm \sqrt{4y^2 - 4}}{2} $$
$$ e^x \;=\; y \pm \sqrt{y^2 - 1} $$
So,
$$ y^2 \ge 1 \;as\; y \ge 0, \;it \; follows \; that \; y \ge 1 $$
How to Use Hyperbolic Function Calculator?
Hyperbolic functions calculator has a user-friendly interface that enables everyone to easily use this calculator to solve hyperbolic function problems.
You should check our guidelines before using this hyperbolic trig calculator so that you do not have any difficulty in the calculation process. These guidelines are:
- Enter your hyperbolic function in the input field of the hyperbolic sine calculator.
- Review your input function before hitting the calculate button.
- Click on the “Calculate” button of hyperbolic tangent calculator to get solution.
- Press the “Recalculate” button that brings you back to a new page for the calculation of more hyperbolic questions.
Results from Hyperbolic Trig Calculator:
You will get the result of the hyperbolic function according to your given input (even if you can give all types of hyperbolic functions identities) from the Hyperbolic function calculator. It may include as
- Result box
Result box of the hyperbolic calculator provides the solution of your given hyperbolic trigonometric function when you press the result option.
- Possible steps option
Steps give you a solution of the hyperbolic problem in a step-by-step method with an explanation.
Advantages of Hyperbolic Tangent Calculator:
The hyperbolic functions calculator provides you with millions of benefits while using it to calculate hyperbolic functions identities. You just need to enter your algebraic hyperbolic function and you get the result in no time. These advantages are:
- It is a trustworthy tool as it always provides precise results with less or no human error in the calculation.
- Our hyperbolic calculator is a speedy tool that provides solutions for hyperbolic functions in less than time.
- You do not need to pay any fee because the hyperbolic trig calculator is a free online tool to find the solution of algebraic hyperbolic functions.
- You can use the hyperbolic cosine calculator for more practice of hyperbolic questions so that you get a strong hold on its conceptual method
- Hyperbolic function calculator has a user-friendly interface even a beginner can use it easily to calculate the hyperbolic functions.
