Cotangent, defined

The dissipation factor is a ratio of the real power (in-phase power) to the reactive power (power 90° out of phase). It is also defined as (1) IT is the ratio of conductance of a capacitor in which the material is the dielectric to its susceptance, (2) IT is the ratio of its parallel reactance to its parallel resistance it is the tangent of the loss angle and the cotangent... 

A more general theoretical model [29], which results in Equation 11.38, provides a better description of an elastomeric stress-strain curve all the way up to fracture, by including the finite extensibilities of the chains. In this equation, 1 is the inverse Langevin function. " is a transcendental function which is defined by Equation 11.39. Coth is the hyperbolic cotangent function. The superscript of -1 represents the functional inversion (and not merely simple reciprocal) of the function in square brackets. 

In this section we define the "naive" relative cotangent complex in the special context in which we shall need it. The word "naive" is used to distinguish the complex which we define, from that defined in general by Illusie [17], although in this special case his definition agrees with the one which we will adopt. 

It is also possible to define cofunctions in analogy with Eq. (4.10), namely the cotangent and cosecant ... 

There are many practical applications in engineering for the trigonometric functions sine, cosine, tangent, secant, cosecant, and cotangent. These functions are defined as the ratios of the sides of plane right triangles. These functions are shown in Table 7.12. 

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