# How to use *Trigonometry* in a sentence

The introduction of hyperbolic functions into

**trigonometry**was also due to him.Beyond this point, analytical methods must be adopted, and the student passes to

**trigonometry**and the infinitesimal calculus.By means of this instrument questions in navigation,

**trigonometry**, &c., are solved with the aid of a pair of compasses.Ptolemaei magnam compositionem (printed at Venice in 1496), and his own De Triangulis (Nuremberg, 1533), the earliest work treating of

**trigonometry**as a substantive science.In "geodesy," and the cognate subject "figure of the earth," the matter of greatest moment with regard to the sphere is the determination of the area of triangles drawn on the surface of a sphere - the so-called "spherical triangles"; this is a branch of

**trigonometry**, and is studied under the name of spherical**trigonometry**.AdvertisementIn 1833 he published Elements of

**Trigonometry**.Complex numbers are conveniently treated in connexion not only with the theory of equations but also with analytical

**trigonometry**, which suggests the graphic representation of a+b,l - by a line of length (a 2 +b 2)i drawn in a direction different from that of the line along which real numbers are represented.The earlier editions did not contain the

**trigonometry**.The second and third volumes include also his correspondence with his contemporaries; and there is a tract on

**trigonometry**by Caswell.Perhaps to the student there is no part of elementary mathematics so repulsive as is spherical

**trigonometry**.AdvertisementAmong these subjects were the transit of Mercury, the Aurora Borealis, the figure of the earth, the observation of the fixed stars, the inequalities in terrestrial gravitation, the application of mathematics to the theory of the telescope, the limits of certainty in astronomical observations, the solid of greatest attraction, the cycloid, the logistic curve, the theory of comets, the tides, the law of continuity, the double refraction micrometer, various problems of spherical

**trigonometry**, &c. In 1742 he was consulted, with other men of science, by the pope, Benedict XIV., as to the best means of securing the stability of the dome of St Peter's, Rome, in which a crack had been discovered.Simple Calculation of Shadows Shadow length can be calculated quite simply using

**trigonometry**.In that year Adriaan van Roomen gave out as a problem to all mathematicians an equation of the 45 th degree, which, being recognized by Vieta as depending on the equation between sin 4 and sin 43/45, was resolved by him at once, all the twenty-three positive roots of which the said equation was capable being given at the same time (see

**Trigonometry**).It is a Treatise on

**Trigonometry**, by a Scotsman, James Hume of Godscroft, Berwickshire, a place still in possession of the family of Hume.In the case of more considerable distances, however, a globe of suitable size should be consulted, or - and this seems preferable - they should be calculated by the rules of spherical

**trigonometry**.AdvertisementDuring this period logarithms were invented,

**trigonometry**and algebra developed, analytical geometry invented, dynamics put upon a sound basis, and the period closed with the magnificent invention of (or at least the perfecting of) the differential calculus by Newton and Leibnitz and the discovery of gravitation.His earliest publications, beginning with A Syllabus of Plane Algebraical Geometry (1860) and The Formulae of Plane

**Trigonometry**(1861), were exclusively mathematical; but late in the year 1865 he published, under the pseudonym of "Lewis Carroll," Alice's Adventures in Wonderland, a work that was the outcome of his keen sympathy with the imagination of children and their sense of fun.Todhunter also published keys to the problems in his textbooks on algebra and

**trigonometry**; and a biographical work, William Whewell, account of his writings and correspondence (1876), in addition to many original papers in scientific journals.With Vieta, by reason of the advance in arithmetic, the style of treatment becomes more strictly trigonometrical; indeed, the Universales Inspectiones, in which the calculation occurs, would now be called plane and spherical

**trigonometry**, and the accompanying Canon mathematicus a table of sines, tangents and secants.'The generalized view of angles and their measurement is treated in the article

**Trigonometry**.AdvertisementNewton tells us himself that, when he had purchased a book on astrology at Stourbridge fair, a fair held close to Cambridge, he was unable, on account of his ignorance of

**trigonometry**, to understand a figure of the heavens which was drawn in this book.The work on [[

**Trigonometry**]] and Double Algebra (1849) contains in the latter part a most luminous and philosophical view of existing and possible systems of symbolic calculus.He applied Alexandrian

**trigonometry**to estimate the distances and sizes of the sun and moon, and also postulated a heliocentric universe.Whenever triangles turn up, you need to know

**trigonometry**to deal with them.He shows how Greek astronomers developed the first true

**trigonometry**.AdvertisementIf the parallax angle of a star is known then its distance can be calculated by

**trigonometry**.These texts were the precursors of spherical

**trigonometry**, which became vital to astronomy.Continue geometry, including Pythagoras ' Theorem and basic

**trigonometry**.The use of these simple

**trigonometry**is illustrated by the method of calculating distances on the Earth.Thanks to some brilliant Australian dude, we now have " rational

**trigonometry**" .AdvertisementRelationships and common formulae from elementary

**trigonometry**, including the basic properties of sine and cosine.These calculations are little more than three-dimensional

**trigonometry**in most cases involving converting tape, compass and clino measurements into an XYZ vector.Triangulation A method of determining the location of an unknown point, as in GPS navigation, by using the laws of plane

**trigonometry**.Besides the logarithms and the calculating rods or bones, Napier's name is attached to certain rules and formulae in spherical

**trigonometry**.He published, among other mathematical works, Clavis Mathematica, in 1631, in which he introduced new signs for certain mathematical operations (see Algebra); a treatise on navigation entitled Circles of Proportion, in 1632; works on

**trigonometry**and dialling, and his Opuscula Mathematica, published posthumously in 1676.AdvertisementThis work included the "Logometria," the trigonometrical theorem known as "Cotes' Theorem on the Circle" (see

**TRIGONOMETRY**), his theorem on harmonic means, subsequently developed by Colin Maclaurin, and a discussion of the curves known as "Cotes' Spirals," which occur as the path of a particle described under the influence of a central force varying inversely as the cube of the distance.This contained work on planar and spherical

**trigonometry**originally done much earlier in about 1464.Thanks to some brilliant Australian dude, we now have " rational

**trigonometry**".Last week, I needed to decipher an engineer 's property description, and did not have to haul out my old

**trigonometry**book.One tab is for

**trigonometry**and geometry functions, the second tab is for higher math functions and the third tab is for numbers you place in memory.AdvertisementThis can be especially difficult as a child begins high school and has to tackle difficult subjects, such as long forgotten

**trigonometry**or advanced chemistry.For the subjects of this heading see the articles DIFFERENTIAL EQUATIONS; FOURIER'S SERIES; CONTINUED FRACTIONS; FUNCTION; FUNCTION OF REAL VARIABLES; FUNCTION COMPLEX; GROUPS, THEORY OF; INFINITESIMAL CALCULUS; MAXIMA AND MINIMA; SERIES; SPHERICAL HARMONICS;

**TRIGONOMETRY**; VARIATIONS, CALCULUS OF.For the subjects under this heading see the articles CONIC SECTIONS; CIRCLE; CURVE; GEOMETRICAL CONTINUITY; GEOMETRY, Axioms of; GEOMETRY, Euclidean; GEOMETRY, Projective; GEOMETRY, Analytical; GEOMETRY, Line; KNOTS, MATHEMATICAL THEORY OF; MENSURATION; MODELS; PROJECTION; Surface;

**Trigonometry**.It thus came about that while some progress was made in algebra, the talents of the race were bestowed on astronomy and

**trigonometry**.A

**trigonometry**(Doctrina triangulorum,) by him was published a year after his death.AdvertisementThe best known of these, which is called Legendre's theorem, is usually given in treatises on spherical

**trigonometry**; by means of it a small spherical triangle may be treated as a plane triangle, certain corrections being applied to the angles.In Albertus Magnus the name Geber occurs only once and then with the epithet "of Seville"; doubtless the reference is to the Arabian Jabir ben Aflah, who lived in that city in the r r th century, and wrote an astronomy in 9 books which is of importance in the history of

**trigonometry**.During his tenure of this chair he published two volumes of a Course of Mathematics - the first, entitled Elements of Geometry, Geometrical Analysis and Plane

**Trigonometry**, in 1809, and the second, Geometry of Curve Lines, in 1813; the third volume, on Descriptive Geometry and the Theory of Solids was never completed.We find that geometry was neglected except in so far as it was of service to astronomy;

**trigonometry**was advanced, and algebra improved far beyond the attainments of Diophantus.For fuller discussion reference should be made to Geometry and

**Trigonometry**, as well as to the articles dealing with particular figures, such as Triangle, Circle, &C.AdvertisementBut every quaternion formula is a proposition in spherical (sometimes degrading to plane)

**trigonometry**, and has the full advantage of the symmetry of the method.