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In the 2nd century AD, the Greco-Egyptian astronomer Ptolemy (from Alexandria, Egypt) constructed detailed trigonometric tables (Ptolemy's table of chords) in Book 1, chapter 11 of his Almagest. [11] Ptolemy used chord length to define his trigonometric functions, a minor difference from the sine convention we use today. [12] (The value we call ...
There are several equivalent ways for defining trigonometric functions, and the proofs of the trigonometric identities between them depend on the chosen definition. The oldest and most elementary definitions are based on the geometry of right triangles and the ratio between their sides.
Another important application of trigonometric tables and generation schemes is for fast Fourier transform (FFT) algorithms, where the same trigonometric function values (called twiddle factors) must be evaluated many times in a given transform, especially in the common case where many transforms of the same size are computed. In this case ...
Laplace's equations are important in many areas of physics, including electromagnetic theory, heat transfer, and fluid dynamics. The basic hyperbolic functions are: [1] hyperbolic sine " sinh" (/ ˈ s ɪ ŋ, ˈ s ɪ n tʃ, ˈ ʃ aɪ n /), [2] hyperbolic cosine " cosh" (/ ˈ k ɒ ʃ, ˈ k oʊ ʃ /), [3] from which are derived: [4]
In the late 11th century, Omar Khayyám (1048–1131) solved cubic equations using approximate numerical solutions found by interpolation in trigonometric tables. In the 13th century, Naṣīr al-Dīn al-Ṭūsī was the first to treat trigonometry as a mathematical discipline independent from astronomy, and he developed spherical trigonometry ...
[1] [10] Another precarious convention used by a small number of authors is to use an uppercase first letter, along with a “ −1 ” superscript: Sin −1 (x), Cos −1 (x), Tan −1 (x), etc. [11] Although it is intended to avoid confusion with the reciprocal, which should be represented by sin −1 (x), cos −1 (x), etc., or, better, by ...
Classical physics traditionally includes the fields of mechanics, optics, electricity, magnetism, acoustics and thermodynamics. The term Modern physics is normally used for fields which rely heavily on quantum theory , including quantum mechanics , atomic physics , nuclear physics , particle physics and condensed matter physics .
Hipparchus (/ h ɪ ˈ p ɑːr k ə s /; Greek: Ἵππαρχος, Hípparkhos; c. 190 – c. 120 BC) was a Greek astronomer, geographer, and mathematician.He is considered the founder of trigonometry, [1] but is most famous for his incidental discovery of the precession of the equinoxes. [2]