Trig functions



Circle based trig:

sine function

sin(theta) = b

cosine function

cos(theta) = c

tangent function:

tan(theta) = b/c


Hyperbolic trig:

The Hyperbolic functions Sinh, Cosh, and Tanh

As Sin and Cos and Tan  functions, Sinh and Cosh have a simple geometrical interpretation;


hyperbolic sine function

sinh(theta) = b

hyperbolic cosine function

cosh(theta) = c

hyperbolic tangent function

tanh(theta) = b/c

Hyperbolic functions are useful because they occur in the solutions of some important linear differential equations, notably that defining the shape of a hanging cable, the catenary, and Laplace's equation (in Cartesian coordinates), which is important in many areas of physics including electromagnetic theory, heat transfer, fluid dynamics, and special relativity.