Dictionary
the mathematics of triangles and trigonometric functions
|
Wikipedia
Trigonometry (from the Greek languageGreek ''trigonon'' = three angles and ''metro'' = measure) is a branch of mathematics dealing with angles, triangle (geometry)triangles and trigonometric functions such as sine, cosine and tangent. It has some relationship to geometry, though there is disagreement on exactly what that relationship is; for some, trigonometry is just a subtopic of geometry.
Early history - The origins of trigonometry trace to the cultures of the ancient Egyptians and Babylonians and Indus Valley civilizations, over 3000 years ago. Indian mathematicians were the pioneers of variable computations algebra for use in astronomical calculations along with trigonometry. Lagadha is the only known mathematician today to have used geometry and trigonometry for astronomy in his book Vedanga Jyotisha, much of whose works were destroyed by foreign invaders of India.Greek mathematician Hipparchus (astronomer)Hipparchus circa 150 BC compiled a trigonometric table for solving triangles.Another Greek mathematician, Ptolemy circa 100 AD further developed trigonometric calculations.The SilesiaSilesian mathematician Bartholemaeus Pitiscus published an influential work on trigonometry in 1595 and introduced the word to the English and French languages.
Trigonometry today - There are an enormous number of uses of trigonometryapplications of trigonometry. Of particular value is the technique of triangulation which is used in astronomy to measure the distance to nearby stars, in geography to measure distances between landmarks, and in satellite navigation systems. Other fields which make use of trigonometry include astronomy (and hence navigation, on the oceans, in aircraft, and in space), music theory, acoustics, optics, analysis of financial markets, electronics, probability theory, statistics, biology, medical imaging (CAT scans and ultrasound), pharmacy, chemistry, number theory (and hence cryptology), seismology, meteorology, oceanography, many physical sciences, land surveying and geodesy, architecture, phonetics, economics, electrical engineering, mechanical engineering, civil engineering, computer graphics, cartography, crystallography.A modern envisioning of trigonometry - rational trigonometry, involving "spread" and "quadrance" instead of angles and length - has been devised by Dr. Norman J. WildbergerNorman Wildberger of the University of New South Wales.
About trigonometry - wikibooksparAlgebraTrigonometry Two triangles are said to be similarity (mathematics)#geometrysimilar if one can be obtained by uniformly expanding the other. This is the case if and only if their corresponding angles are equal, and it occurs for example when two triangles share an angle and the sides opposite to that angle are parallel. The crucial fact about similar triangles is that the lengths of their sides are proportionate. That is, if the longest side of a triangle is twice that of the longest side of a similar triangle, say, then the shortest side will also be twice that of the shortest side of the other triangle, and the median side will be twice that of the other triangle. Also, the ratio of the longest side to the shortest in the first triangle will be the same as the ratio of the longest side to the shortest in the other triangle. Using these facts, one defines trigonometric functions, starting with right triangles, triangles with one right angle (90 degree (angle)degrees or Piπ/2 radians). The longest side in any triangle is the side opposite the largest angle.Because the sum of the angles in a triangle is 180 degrees or π radians, the largest angle in such a triangle is the right angle.The longest side in such a triangle is therefore the side opposite the right angle and is called the hypotenuse.Pick two ''right angled triangles'' which share a second angle ''A''. These triangles are necessarily similar, and the ratio of the side opposite to ''A'' to the hypotenuse will therefore be the same for the two triangles. It will be a number between 0 and 1 which depends only on ''A''; we call it the sine of A and write it as sin(''A''). Similarly, one can define the cosine of ''A'' as the ratio of the side adjacent to ''A'' to the hypotenuse.:These are by far the most important trigonometric functions; other functions can be defined by taking ratios of other sides of the right triangles but they can all be expressed in terms of sine and cosine. These are the tangent, secant, cotangent, and cosecant.::The ''sine'', ''cosine'' and ''tangent'' ratios in right triangles can be remembered by SOH CAH TOA (sine-opposite-hypotenuse cosine-adjacent-hypotenuse tangent-opposite-adjacent). It is commonly referred to as Sohcahtoa by math teachers, who liken it to a (non existant) native american girl's name. See trigonometry mnemonics for other mnemonics.So far, the trigonometric functions have been defined for angles between 0 and 90 degrees (0 and π/2 radians) only. Using the unit circle, one may extend them to all positive and negative arguments (see trigonometric function).Once the sine and cosine functions have been tabulated (or computed by a calculator), one can answer virtually all questions about arbitrary triangles, by using the law of sines and the law of cosines. These laws can be used to compute the remaining angles and sides of any triangle as soon as two sides and an angle or two angles and a side or three sides are known.Some mathematicians believe that trigonometry was originally invented to calculate sundials, a traditional exercise in the oldest books. It is also very important for surveying.
See also - Trigonometric !identitiesCategory:Trigonometr y ar:علم !المثلثاتca:Trigonometr iada:Trigonometride:Trigonomet riees:Trigonometríaeo:Trigono metriofr:Trigonométrieit:Trig onometriahe:טריגונומט ריהlt:Trigonometrijanl:Goni ometrieid:Trigonometrija:三 法pl:Trygonometriapt:Trigono metriaru:Тригономет ияsk:Trigonometriasl:Trigon ometrijafi:Trigonometriath:ต รีโกณมิติtr: Trigonometrizh:三角学
|
|
Websites
All Elementary Mathematics
Web high mathematical school. All sections of curriculum of elementary mathematics. Arithmetic, algebra, geometry, trigonometry,functions and graphs, analysis. Theory and solving problems. Versions of examination tests. Online consulting. Preparatory to universities and colleges.
http://www.bymath.com/
The MathRoom.ca
Online math lessons and tutoring for High School and College math students
http://www.the-mathroom.ca/
DZynSource for Molds
DZynSource for Molds is engineering software for mold designers, tooling engineers, or anyone involved in the engineering aspect of mold design or moldmaking. It is designed to speed up the engineering equation process. DZynSource for Molds automates most of the calculations that commonly arise during the design, checking, and troubleshooting of molds. Users can choose the calculation to perform, enter the known data, and then press 'Calculate'. The answers are displayed in easy to read diagrams with no complicated formulas or equations, a spokesperson stated. Key features of the software include: 8 basic D.C. electrical calculations Fluid calculations, including pressure losses, bubbler sizing, continuity equation, equivalent hydraulic diameter, hydraulic cylinder calculations, and Reynolds Number Galvanic table and a hot runner checklist Mechanical properties of 30 common moldmaking metals, including steels, and aluminum and copper alloys Sizes, properties, and torque values for inch and metric screws Strength of materials calculations, including plate deformation, beam deflection and stresses, hoop stress and expansion, elastic stress and strain; also moment of inertia, section modulus, and radius of gyration for 10 common geometric shapes Thermal expansion includes coefficients for the 30 common moldmaking metals, including calculations for expansion, initial size or final size Vent width calculator Production quantity, production-time, and number of cavities calculations. Tooling ball, roll dimension, chord, and 3-sided cutter calculations
http://www.dzynsource.com/
Clark University Department of Mathematics and Computer Science
"Aleph0". Searchable course catalog, faculty and some students home pages. Online interactive features: Euclid's elements Java applets, short Trig course, Mandelbrot and Julia set explorer, Newton basins generator, math problems of David Hilbert. Worcester.
http://aleph0.clarku.edu/
S.O.S. Math
Contains tutorials covering algebra, geometry, calculus, differential equations, matrices, and complex variables. Reviews the most important results, techniques and formulas. Presented in worksheet format and require active participation. Includes practice quizzes and forum board.
http://www.sosmath.com/
Ping
A Belgian company providing high quality Internet access over classical PSTN lines, as well as ISDN, and has since recently extended this with the V90 capability for PSTN modems.
http://www.ping.be/
|
|