sinh(x)
The sinh(x) function, also known as the hyperbolic sine function, is a mathematical function that is the hyperbolic analog of the traditional sine function
The sinh(x) function, also known as the hyperbolic sine function, is a mathematical function that is the hyperbolic analog of the traditional sine function. It is defined as:
sinh(x) = (e^x – e^(-x)) / 2
where e is Euler’s number approximately equal to 2.71828.
The sinh(x) function can be thought of in terms of the exponential function. It is an odd function, symmetrical about the origin, and has a graph that looks similar to a parabola. The values of sinh(x) grow exponentially as x increases.
Some properties of sinh(x) include:
1. sinh(0) = 0
2. sinh(x) is an odd function, which means sinh(-x) = -sinh(x)
3. The range of sinh(x) is all real numbers. As x approaches positive or negative infinity, sinh(x) approaches infinity.
4. sinh(x) satisfies the hyperbolic identity: sinh^2(x) + cosh^2(x) = 1
The sinh(x) function is commonly used in various mathematical and scientific applications, such as in the study of oscillatory systems, differential equations, and the theory of relativity. It has important connections to other hyperbolic functions, such as cosh(x) and tanh(x), and can be used in trigonometric substitutions for integrals.
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