In Exercises 1–6, evaluate the function. If the value is not...

In Exercises 1–6, evaluate the function. If the value is not a rational number, round your answer to three decimal places.
$$
\begin{array}{l}{\text { (a) } \sinh 3} \\ {\text { (b) } \tanh (-2)}\end{array}
$$

Key Concepts

Hyperbolic Functions

Hyperbolic functions are analogues of the ordinary trigonometric, or circular, functions but relate to hyperbolas rather than circles. They are defined in terms of exponential functions and include functions such as sinh, cosh, and tanh. These functions have unique properties and identities that are used in various areas of mathematics and science.

Exponential Function

The exponential function, often expressed as e raised to a power, is fundamental in defining hyperbolic functions. The definitions of sinh and cosh, for example, are based on combinations of exponential expressions, which allow these functions to capture both growth and oscillatory behavior in different contexts.

Function Evaluation

Function evaluation involves substituting a specific value into a function’s expression to determine its output. This process requires understanding the function’s definition and simplifying the result, which in many cases involves combining algebraic manipulation with numerical approximation techniques.

Numerical Rounding

Numerical rounding is the process of adjusting a numerical value to a specified degree of accuracy, often due to the impracticality of representing irrational numbers exactly. When a computed value is not a rational number, it is common practice to round the result to a certain number of decimal places to facilitate easier interpretation and communication.

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