# branches of trigonometry

[17][18][19] Nasīr al-Dīn al-Tūsī was the first to treat trigonometry as a mathematical discipline independent from astronomy, and he developed spherical trigonometry into its present form. Arithmetic: This is the oldest and most basic form of mathematics. Arithmetic chiefly concerns the addition, subtraction, multiplication and division of real numbers that aren't negative. Since any two right triangles with the same acute angle A are similar[29], the value of a trigonometric ratio depends only on the angle A. By the 10th century, Islamic mathematicians were using all six trigonometric functions, had tabulated their values, and were applying them to problems in spherical geometry. [33], Trigonometric ratios can also be represented using the unit circle, which is the circle of radius 1 centered at the origin in the plane. Q(a,b) is any point on the circle with angle SOQ = x radian. There are many branches of mathematics namely Algebra, Geometry, Arithmetic, Trigonometry, calculus etc. [57], In land surveying, trigonometry is used in the calculation of lengths, areas, and relative angles between objects. Likewise, many branches of mathematics play a part in the tower of math. In spherical trigonometry, students study curved triangles drawn on the surface of a sphere. Driven by the demands of navigation and the growing need for accurate maps of large geographic areas, trigonometry grew into a major branch of mathematics. [23] At the same time, another translation of the Almagest from Greek into Latin was completed by the Cretan George of Trebizond. In the 3rd century BC, Hellenistic mathematicians such as Euclid and Archimedes studied the properties of chords and inscribed angles in circles, and they proved theorems that are equivalent to modern trigonometric formulae, although they presented them geometrically rather than algebraically. See below under Mnemonics. Mathematics is broadly divided into pure mathematics and applied mathematics. See List of trigonometric identities for more relations between these functions. Trigonometry deals with relationships between the sides and the angles of triangles and with the trigonometric functions, which describe those relationships, as well as describing angles in general and the motion of waves such as sound and light waves. [9] They, and later the Babylonians, studied the ratios of the sides of similar triangles and discovered some properties of these ratios but did not turn that into a systematic method for finding sides and angles of triangles. [78], Trigonometry has been noted for its many identities, that is, equations that are true for all possible inputs.[80]. [82], The law of sines (also known as the "sine rule") for an arbitrary triangle states:[83]. Trigonometry (from Greek trigōnon, "triangle" and metron, "measure"[1]) is a branch of mathematics that studies relationships between side lengths and angles of triangles. Festival of Sacrifice: The Past and Present of the Islamic Holiday of Eid al-Adha. . Trigonometry is one of the important branches in the history of mathematics and this concept is given by a Greek mathematician Hipparchus. For understanding the concept of radian measure and trigonometric functions, we need to first analyse the figure given below: The figure above is of a circle with centre O, that lies at the origin of coordinate axes. "Islamic astronomy." [11] 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. is the area of the triangle and R is the radius of the circumscribed circle of the triangle: The law of cosines (known as the cosine formula, or the "cos rule") is an extension of the Pythagorean theorem to arbitrary triangles:[83]. Scientific American 254.4 (1986): 74-83, A sentence more appropriate for high schools is "', harvtxt error: multiple targets (3×): CITEREFBoyer1991 (. Bulletin of the American Mathematical Society 54.11 (1948): 1013-1041. [34] This representation allows for the calculation of commonly found trigonometric values, such as those in the following table:[35]. These include the chord (crd(θ) = 2 sin(θ/2)), the versine (versin(θ) = 1 − cos(θ) = 2 sin2(θ/2)) (which appeared in the earliest tables[51]), the coversine (coversin(θ) = 1 − sin(θ) = versin(π/2 − θ)), the haversine (haversin(θ) = 1/2versin(θ) = sin2(θ/2)),[52] the exsecant (exsec(θ) = sec(θ) − 1), and the excosecant (excsc(θ) = exsec(π/2 − θ) = csc(θ) − 1). Δ {\displaystyle y=\sin A} , produces the following analytical identities for sine, cosine, and tangent in terms of e and the imaginary unit i: Other commonly used trigonometric identities include the half-angle identities, the angle sum and difference identities, and the product-to-sum identities. [3], Throughout history, trigonometry has been applied in areas such as geodesy, surveying, celestial mechanics, and navigation. The following trigonometric identities are related to the Pythagorean theorem and hold for any value:[86]. The adjacent leg is the other side that is adjacent to angle A. Since the triangles are all located on a plane, the sum of the angles is always 180 degrees. [26] Gemma Frisius described for the first time the method of triangulation still used today in surveying. Centuries passed before more detailed tables were produced, and Ptolemy's treatise remained in use for performing trigonometric calculations in astronomy throughout the next 1200 years in the medieval Byzantine, Islamic, and, later, Western European worlds. Another method is to expand the letters into a sentence, such as "Some Old Hippie Caught Another Hippie Trippin' On Acid". Using the unit circle, one can extend the definitions of trigonometric ratios to all positive and negative arguments[36] (see trigonometric function). But if you still find it difficult to understand these branches, then you can get help from math experts. These ratios are given by the following trigonometric functions of the known angle A, where a, b and c refer to the lengths of the sides in the accompanying figure: The hypotenuse is the side opposite to the 90 degree angle in a right triangle; it is the longest side of the triangle and one of the two sides adjacent to angle A. Biography – Encyclopaedia Iranica", From Kant to Hilbert: a source book in the foundations of mathematics, "JPEG Standard (JPEG ISO/IEC 10918-1 ITU-T Recommendation T.81)", Lecture 3 | Quantum Entanglements, Part 1 (Stanford), Khan Academy: Trigonometry, free online micro lectures, Trigonometry, by Michael Corral, Covers elementary trigonometry, Distributed under GNU Free Documentation License, https://en.wikipedia.org/w/index.php?title=Trigonometry&oldid=991241982, Wikipedia indefinitely semi-protected pages, Wikipedia indefinitely move-protected pages, Short description is different from Wikidata, Creative Commons Attribution-ShareAlike License, This page was last edited on 29 November 2020, at 01:32. [14] These Greek and Indian works were translated and expanded by medieval Islamic mathematicians. A ... Start applying these basic mathematics branches and start getting a good command over them.

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