sech x
The term “sech x” refers to the hyperbolic secant function, often denoted as sech(x)
The term “sech x” refers to the hyperbolic secant function, often denoted as sech(x). It is a mathematical function that is part of a family of hyperbolic functions. The hyperbolic secant function is defined as:
sech(x) = 1 / cosh(x)
where cosh(x) represents the hyperbolic cosine function. The hyperbolic cosine function is defined as:
cosh(x) = (e^x + e^(-x)) / 2
where e is Euler’s number, approximately equal to 2.71828.
In simpler terms, the hyperbolic secant of an angle x is obtained by taking the inverse of the hyperbolic cosine of that angle.
The graph of the hyperbolic secant function exhibits a similar shape to the graph of the regular secant function in trigonometry, but it is smoother and symmetric with respect to the y-axis. The range of the hyperbolic secant function is always between 1 and positive infinity.
It is often used in calculus and differential equations, as well as in various branches of physics and engineering. The hyperbolic secant function is particularly useful in the analysis of systems with exponential growth or decay.
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