# Portal:Analysis

## Analysis

**Analysis** is the process of breaking a complex topic or substance into smaller parts to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle, though *analysis* as a formal concept is a relatively recent development. As a formal concept, the method has variously been ascribed to Ibn al-Haytham, Descartes (*Discourse on the Method*), Galileo, and Newton, as a practical method of physical discovery.

## Selected article

In mathematics, the **trigonometric functions** (also called circular functions) are functions of an angle. They are important in the study of triangles and modeling periodic phenomena, among many other applications. Trigonometric functions are commonly defined as ratios of two sides of a right triangle containing the angle, and can equivalently be defined as the lengths of various line segments from a unit circle. More modern definitions express them as infinite series or as solutions of certain differential equations, allowing their extension to arbitrary positive and negative values and even to complex numbers.

In modern usage, there are six basic trigonometric functions, which are tabulated here along with equations relating them to one another. Especially in the case of the last four, these relations are often taken as the *definitions* of those functions, but one can define them equally well geometrically or by other means and then derive these relations.

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The **Mathematics WikiProject** is the center for mathematics-related editing on Wikipedia. Join the discussion on the project's **talk page**.

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## Selected picture

In complex dynamics, the **Julia set** of a holomorphic function informally consists of those points whose long-time behavior under repeated iteration of can change drastically under arbitrarily small perturbations. Above is a 3D slice of a 4D Julia set.

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## Did you know?

- ...that the Gudermannian function relates the circular trigonometric functions and the hyperbolic trigonometric functions without the use of complex numbers?

## Categories

*Topics in Analysis*

General | Calculus | Differentiation | Integration |
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Functions | Harmonic/Fourier analysis | Measure theory | Miscellaneous |

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