Mathematics

Geometric Interpretation

 

The trigonometric functions are derived from an orthogonal triangle which is based on the Euclidean geometry. In non Euclidean geometry we may have an orthogonal triangle in which the summation of its angles may not be 180 degrees, it is always less than 180 degrees. This is because its sides can be curved, so the angles are narrowed. In this case we define the hyperbolic trigonometric functions.

Consider the Cartesian system and the hyperbolic function

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Graphical Representation

 

The six hyperbolic functions are represented graphically in the following images. The amplitude is on the y axis and the angle is on the x axis, in degrees. Often the angle is also represented in radians. One radian (π) is equal to 180 degrees.

We have to keep in mind that these functions are not periodic. As the positive angle increases or the negative angle decreases, the amplitude continues its trend without repeating itself.

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