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Exsecant
The exsecant (exsec, exs) and excosecant (excosec, excsc, exc) are trigonometric functions defined in terms of the secant and cosecant functions. They used to be important in fields such as surveying, railway engineering, civil engineering, astronomy, and spherical trigonometry and could help improve accuracy, but are rarely used today except to simplify some calculations. Exsecant The exsecant, (Latin: ''secans exterior'') also known as exterior, external, outward or outer secant and abbreviated as exsec or exs, is a trigonometric function defined in terms of the secant function sec(''θ''): \operatorname(\theta) = \sec(\theta) - 1 = \frac - 1. The name ''exsecant'' can be understood from a graphical construction of the various trigonometric functions from a unit circle, such as was used historically. sec(''θ'') is the secant line , and the exsecant is the portion of this secant that lies ''exterior'' to the circle (''ex'' is Latin for ''out of''). Excosecant A relat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exsecant And Excosecant Plot
The exsecant (exsec, exs) and excosecant (excosec, excsc, exc) are trigonometric functions defined in terms of the secant and cosecant functions. They used to be important in fields such as surveying, railway engineering, civil engineering, astronomy, and spherical trigonometry and could help improve accuracy, but are rarely used today except to simplify some calculations. Exsecant The exsecant, (Latin: ''secans exterior'') also known as exterior, external, outward or outer secant and abbreviated as exsec or exs, is a trigonometric function defined in terms of the secant function sec(''θ''): \operatorname(\theta) = \sec(\theta) - 1 = \frac - 1. The name ''exsecant'' can be understood from a graphical construction of the various trigonometric functions from a unit circle, such as was used historically. sec(''θ'') is the secant line , and the exsecant is the portion of this secant that lies ''exterior'' to the circle (''ex'' is Latin for ''out of''). Excosecant A rela ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Versine
The versine or versed sine is a trigonometric function found in some of the earliest (Sanskrit Āryabhaṭa's sine table , ''Aryabhatia'', Section I) trigonometric tables. The versine of an angle is 1 minus its cosine. There are several related functions, most notably the coversine and haversine. The latter, half a versine, is of particular importance in the haversine formula of navigation. Overview The versine or versed sine is a trigonometric function already appearing in some of ...[...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Surveying
Surveying or land surveying is the technique, profession, art, and science of determining the terrestrial two-dimensional or three-dimensional positions of points and the distances and angles between them. A land surveying professional is called a land surveyor. These points are usually on the surface of the Earth, and they are often used to establish maps and boundaries for ownership, locations, such as the designed positions of structural components for construction or the surface location of subsurface features, or other purposes required by government or civil law, such as property sales. Surveyors work with elements of geodesy, geometry, trigonometry, regression analysis, physics, engineering, metrology, programming languages, and the law. They use equipment, such as total stations, robotic total stations, theodolites, GNSS receivers, retroreflectors, 3D scanners, LiDAR sensors, radios, inclinometer, handheld tablets, optical and digital levels, subsurface locators, d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Railway Engineering
Railway engineering is a multi-faceted engineering discipline dealing with the design, construction and operation of all types of rail transport systems. It encompasses a wide range of engineering disciplines, including civil engineering, computer engineering, electrical engineering, mechanical engineering, industrial engineering and production engineering. A great many other engineering sub-disciplines are also called upon. History With the advent of the railways in the early nineteenth century, a need arose for a specialized group of engineers capable of dealing with the unique problems associated with railway engineering. As the railways expanded and became a major economic force, a great many engineers became involved in the field, probably the most notable in Britain being Richard Trevithick, George Stephenson and Isambard Kingdom Brunel. Today, railway systems engineering continues to be a vibrant field of engineering. Subfields *Mechanical engineering * Command, con ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Floating Point
In computing, floating-point arithmetic (FP) is arithmetic that represents real numbers approximately, using an integer with a fixed precision, called the significand, scaled by an integer exponent of a fixed base. For example, 12.345 can be represented as a base-ten floating-point number: 12.345 = \underbrace_\text \times \underbrace_\text\!\!\!\!\!\!^ In practice, most floating-point systems use base two, though base ten (decimal floating point) is also common. The term ''floating point'' refers to the fact that the number's radix point can "float" anywhere to the left, right, or between the significant digits of the number. This position is indicated by the exponent, so floating point can be considered a form of scientific notation. A floating-point system can be used to represent, with a fixed number of digits, numbers of very different orders of magnitude — such as the number of meters between galaxies or between protons in an atom. For this reason, floating-poin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Angle
In Euclidean geometry, an angle is the figure formed by two Ray (geometry), rays, called the ''Side (plane geometry), sides'' of the angle, sharing a common endpoint, called the ''vertex (geometry), vertex'' of the angle. Angles formed by two rays lie in the plane (geometry), plane that contains the rays. Angles are also formed by the intersection of two planes. These are called dihedral angles. Two intersecting curves may also define an angle, which is the angle of the rays lying tangent to the respective curves at their point of intersection. ''Angle'' is also used to designate the measurement, measure of an angle or of a Rotation (mathematics), rotation. This measure is the ratio of the length of a arc (geometry), circular arc to its radius. In the case of a geometric angle, the arc is centered at the vertex and delimited by the sides. In the case of a rotation, the arc is centered at the center of the rotation and delimited by any other point and its image by the rotation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1 (number)
1 (one, unit, unity) is a number representing a single or the only entity. 1 is also a numerical digit and represents a single unit of counting or measurement. For example, a line segment of ''unit length'' is a line segment of length 1. In conventions of sign where zero is considered neither positive nor negative, 1 is the first and smallest positive integer. It is also sometimes considered the first of the infinite sequence of natural numbers, followed by 2, although by other definitions 1 is the second natural number, following 0. The fundamental mathematical property of 1 is to be a multiplicative identity, meaning that any number multiplied by 1 equals the same number. Most if not all properties of 1 can be deduced from this. In advanced mathematics, a multiplicative identity is often denoted 1, even if it is not a number. 1 is by convention not considered a prime number; this was not universally accepted until the mid-20th century. Additionally, 1 is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Subtraction
Subtraction is an arithmetic operation that represents the operation of removing objects from a collection. Subtraction is signified by the minus sign, . For example, in the adjacent picture, there are peaches—meaning 5 peaches with 2 taken away, resulting in a total of 3 peaches. Therefore, the ''difference'' of 5 and 2 is 3; that is, . While primarily associated with natural numbers in arithmetic, subtraction can also represent removing or decreasing physical and abstract quantities using different kinds of objects including negative numbers, fractions, irrational numbers, vectors, decimals, functions, and matrices. Subtraction follows several important patterns. It is anticommutative, meaning that changing the order changes the sign of the answer. It is also not associative, meaning that when one subtracts more than two numbers, the order in which subtraction is performed matters. Because is the additive identity, subtraction of it does not change a number. Subtraction ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Catastrophic Cancellation
In numerical analysis, catastrophic cancellation is the phenomenon that subtracting good approximations to two nearby numbers may yield a very bad approximation to the difference of the original numbers. For example, if there are two studs, one L_1 = 254.5\,\text long and the other L_2 = 253.5\,\text long, and they are measured with a ruler that is good only to the centimeter, then the approximations could come out to be \tilde L_1 = 255\,\text and \tilde L_2 = 253\,\text. These may be good approximations, in relative error, to the true lengths: the approximations are in error by less than 2% of the true lengths, , L_1 - \tilde L_1, /, L_1, < 2\%. However, if the ''approximate'' lengths are subtracted, the difference will be , even though the true difference between the lengths is . The difference of the approximations, |
Trigonometric Functions
In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others. They are among the simplest periodic functions, and as such are also widely used for studying periodic phenomena through Fourier analysis. The trigonometric functions most widely used in modern mathematics are the sine, the cosine, and the tangent. Their reciprocals are respectively the cosecant, the secant, and the cotangent, which are less used. Each of these six trigonometric functions has a corresponding inverse function, and an analog among the hyperbolic functions. The oldest definitions of trigonometric functions, related to right-angle triangles, define them only for acute angles. To extend the sine and cos ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Galileo Galilei
Galileo di Vincenzo Bonaiuti de' Galilei (15 February 1564 – 8 January 1642) was an Italian astronomer, physicist and engineer, sometimes described as a polymath. Commonly referred to as Galileo, his name was pronounced (, ). He was born in the city of Pisa, then part of the Duchy of Florence. Galileo has been called the "father" of observational astronomy, modern physics, the scientific method, and modern science. Galileo studied speed and velocity, gravity and free fall, the principle of relativity, inertia, projectile motion and also worked in applied science and technology, describing the properties of pendulums and "hydrostatic balances". He invented the thermoscope and various military compasses, and used the telescope for scientific observations of celestial objects. His contributions to observational astronomy include telescopic confirmation of the phases of Venus, observation of the four largest satellites of Jupiter, observation of Saturn's rings, and a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer
A computer is a machine that can be programmed to Execution (computing), carry out sequences of arithmetic or logical operations (computation) automatically. Modern digital electronic computers can perform generic sets of operations known as Computer program, programs. These programs enable computers to perform a wide range of tasks. A computer system is a nominally complete computer that includes the Computer hardware, hardware, operating system (main software), and peripheral equipment needed and used for full operation. This term may also refer to a group of computers that are linked and function together, such as a computer network or computer cluster. A broad range of Programmable logic controller, industrial and Consumer electronics, consumer products use computers as control systems. Simple special-purpose devices like microwave ovens and remote controls are included, as are factory devices like industrial robots and computer-aided design, as well as general-purpose devi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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