Hyperbolic trigonometric

Special mathematical functions exponential, logarithm (base 10 and base e), trigonometric, reciprocal trigonometric and hyperbolic trigonometric. 

The ordinary trigonometric functions include the sine, the cosine, the tangent, the cotangent, the secant, and the cosecant. These are sometimes called the circular trigonometric Junctions to distinguish them from the hyperbolic trigonometric functions discussed briefly in the next section of this chapter. 

The other hyperbolic trigonometric functions are the hyperbolic tangent, denoted by tanh(x) the hyperbolic cotangent, denoted by coth(x) the hyperbolic secant, denoted by sech(x) and the hyperbolic cosecant, denoted by csch(x). These functions are given by the equations... 

EXERCISE 2.9 Find the value of each of the hyperbolic trigonometric... 

In this chapter we have introduced symbolic mathematics, which involves the manipulation of symbols instead of performing numerical operations. We have presented the algebraic tools needed to manipulate expressions containing real scalar variables, real vector variables, and complex scalar variables. We have also introduced ordinary and hyperbolic trigonometric functions, exponentials, and logarithms. A brief introduction to the techniques of problem solving was included. 

Hyperbolic trigonometric functions sinh, cosh, tanh.369... 

Substituting these values for Cj and C2 into equation (ix) and writing the exponential terms as hyperbolic trigonometric functions gives... 

The physical property options are labeled as thermo, fluid package, property package, or databank in common process simulators. There are pure-conponent and mixture sections, as well as a databank. For temperature-dependent properties, different functional forms are used (from extended Antione equation to polynomial to hyperbolic trigonometric functions). The equation appears on the physical property screen or in the help utility. 

Figure 2.10 shows the hyperbolic sine and hyperbolic cosine for values of x from 0 to 3. Note that the values of the hyperbolic sin and the hyperbolic cosine do not necessarily lie between -1 and 1 as do the values of the circular sine and cosine functions and that both functions approach e /2 for large values of x. The hyperbolic trigonometric functions are available in Excel. 

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