Problem 1
Question
State the definition of the hyperbolic cosine and hyperbolic sine functions.
Step-by-Step Solution
Verified Answer
Question: Provide the definitions of the hyperbolic cosine and hyperbolic sine functions.
Answer: The hyperbolic cosine function (cosh(x)) is defined as cosh(x) = (e^x + e^{-x}) / 2, and the hyperbolic sine function (sinh(x)) is defined as sinh(x) = (e^x - e^{-x}) / 2, where "e" is the base of the natural logarithm (approximately 2.718) and "x" is the input value for the function.
1Step 1: Definition of Hyperbolic Cosine (cosh) function
The hyperbolic cosine function, denoted by "cosh(x)", is defined in terms of exponential functions as follows:
cosh(x) = \frac{e^x + e^{-x}}{2}
Where "e" is the base of the natural logarithm (approximately equal to 2.718) and "x" is the input value for the function.
2Step 2: Definition of Hyperbolic Sine (sinh) function
The hyperbolic sine function, denoted by "sinh(x)", is defined in terms of exponential functions as follows:
sinh(x) = \frac{e^x - e^{-x}}{2}
Where "e" is the base of the natural logarithm (approximately equal to 2.718) and "x" is the input value for the function.
Other exercises in this chapter
Problem 1
In terms of relative growth rate, what is the defining property of exponential growth?
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What are the domain and range of \(\ln x ?\)
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What is the area of the curved surface of a right circular cone of radius 3 and height \(4 ?\)
View solution Problem 1
Explain the steps required to find the length of a curve \(y=f(x)\) between \(x=a\) and \(x=b.\)
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