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In mathematics, tables of trigonometric functions are useful in a number of areas. Before the existence of pocket calculators, trigonometric tables were essential for navigation, science and engineering. The calculation of mathematical tables was an important area of study, which led to the development of the first mechanical computing devices.
The trigonometric functions of angles that are multiples of 15°, 18°, or 22.5° have simple algebraic values. These values are listed in the following table for angles from 0° to 45°. [1] In the table below, the label "Undefined" represents a ratio If the codomain of the trigonometric functions is taken to be the real numbers these entries ...
Standard normal table. In statistics, a standard normal table, also called the unit normal table or Z table, [ 1 ] is a mathematical table for the values of Φ, the cumulative distribution function of the normal distribution. It is used to find the probability that a statistic is observed below, above, or between values on the standard normal ...
For tables with greater precision (more digits per value), higher order interpolation may be needed to get full accuracy. [3] In the era before electronic computers, interpolating table data in this manner was the only practical way to get high accuracy values of mathematical functions needed for applications such as navigation, astronomy and ...
Basis of trigonometry: if two right triangles have equal acute angles, they are similar, so their corresponding side lengths are proportional.. In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) [1] [2] are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.
List of refractive indices. Refraction at interface. Many materials have a well-characterized refractive index, but these indices often depend strongly upon the frequency of light, causing optical dispersion. Standard refractive index measurements are taken at the "yellow doublet" sodium D line, with a wavelength (λ) of 589 nanometers.
The data below tabulates standard electrode potentials (E °), in volts relative to the standard hydrogen electrode (SHE), at: Absolute partial pressure 101.325 kPa (1.00000 atm; 1.01325 bar) for each gaseous reagent — the convention in most literature data but not the current standard state (100 kPa). Variations from these ideal conditions ...
Abu al-Wafa had sine tables in 0.25° increments, to 8 decimal places of accuracy, and accurate tables of tangent values. [16] He also made important innovations in spherical trigonometry [17] [18] [19] The Persian polymath Nasir al-Din al-Tusi has been described as the creator of trigonometry as a mathematical discipline in its own right.