Trigonometry is…
i) A ration shows approximate sizes of two or more values. Ratios can be shown in different ways. For example 1:3 (one to three), ¼ (one fourth). ii)
* Sine (θ) = Opposite x Hypotunese1
* Cosine (θ) = Adjacent x Hypotunese1
* Tangent (θ) = Opposite x Adjacent 1
iii) You can remember this equations throughout a word SohCahToa Trigonometry came from…
i) The term “trigonometry,” although not of native Greek origin, comes from the Greek word trigonon, meaning “triangle,” and the Greek word metria, meaning“measurement.” As the name implies, trigonometry ultimately developed from the study of right triangles by applying the relationships between the measures of its sides andangles to the study of similar triangles. However, the word “trigonometry” did not exist upon the birth of the subject, but was later introduced by the German mathematician and astronomer, Bartholomaeus Pitiscus in the title of his work, Trigonometria sive de solutione triangularum tractatus brevis et perspicius…, publishedin 1595 ii) In our days, we have a lot of use for trigonometry. We can use trigonometry in Astronomy, geography, engineering, physics and finally mathematics. Trigonometric tables were created over two thousand years ago for studying astronomy. The stars were thought to be fixed on a crystal sphere of great size, and that model was perfect for practical purposes. Only the planets moved on the sphere. The kind of trigonometry needed to understand positions on a sphere is called spherical trigonometry. Spherical trigonometry is rarely taught now since its job has been taken over by linear algebra. However, one of application of trigonometry is astronomy. Physics lays heavy demands on trigonometry. Optics and statics are two early fields of physics that use trigonometry, but all branches of physics use trigonometry since trigonometry aids in understanding space. Related fields such as physical chemistry naturally use...
...Teaching trigonometry using Empirical Modelling
0303417
Abstract
The trigonometric functions sin(x), cos(x) and tan(x) are relationships that exist between the angles
and length of sides in a rightangled triangle. In Empirical Modelling terms, the angles in a triangle
and the length of the sides are observables, and the functions that connect them are the definitions.
These welldefined geometric relationships can be useful when teaching GCSElevel students about
the functions, as they provide a way to visualise what can be thought of as fairly abstract functions.
This paper looks at how different learning styles apply to Empirical Modelling, and presents a practical example of their use in a model to teach trigonometry.
1 Introduction
The trigonometric functions sin(x), cos(x) and tan(x)
are relationships that exist between the angles and
length of sides in a rightangled triangle. In Empirical Modelling terms, the angles in a triangle and the
length of the sides are observables, and the functions
that connect them are the definitions. These welldefined geometric relationships can be useful when
teaching GCSElevel students about the functions,
as they provide a way to visualise what can be
thought of as fairly abstract functions. Rather than
teaching students by showing them diagrams in an
instructive way (already a good way of doing it), a
constructive approach may allow students to gain a...
...Trigonometry (from Greek trigōnon "triangle" + metron "measure"[1]) is a branch of mathematics that studies triangles and the relationships between the lengths of their sides and the angles between those sides. Trigonometry defines the trigonometric functions, which describe those relationships and have applicability to cyclical phenomena, such as waves. The field evolved during the third century BC as a branch of geometry used extensively for astronomical studies.[2] It is also the foundation of the practical art of surveying.
Trigonometry basics are often taught in school either as a separate course or as part of a precalculus course. The trigonometric functions are pervasive in parts of pure mathematics and applied mathematics such as Fourier analysis and the wave equation, which are in turn essential to many branches of science and technology. Spherical trigonometry studies triangles on spheres, surfaces of constant positive curvature, in elliptic geometry. It is fundamental to astronomy and navigation. Trigonometry on surfaces of negative curvature is part of Hyperbolic geometry.
Contents
f one angle of a triangle is 90 degrees and one of the other angles is known, the third is thereby fixed, because the three angles of any triangle add up to 180 degrees. The two acute angles therefore add up to 90 degrees: they are complementary angles. The shape of a triangle is completely determined,...
...Trigonometry (from Greek trigōnon "triangle" + metron"measure"[1]) is a branch of mathematics that studies triangles and the relationships between their sides and the angles between these sides. Trigonometry defines the trigonometric functions, which describe those relationships and have applicability to cyclical phenomena, such as waves. The field evolved during the third century BC as a branch of geometry used extensively for astronomical studies.[2] It is also the foundation of the practical art of surveying.
Trigonometry basics are often taught in school either as a separate course or as part of a precalculus course. The trigonometric functions are pervasive in parts of pure mathematics and applied mathematics such as Fourier analysis and the wave equation, which are in turn essential to many branches of science and technology. Spherical trigonometry studies triangles on spheres, surfaces of constant positive curvature, in elliptic geometry. It is fundamental to astronomy and navigation. Trigonometry on surfaces of negative curvature is part of Hyperbolic geometry.


\History
Main article: History of trigonometry
The first trigonometric tablewas apparently compiled byHipparchus, who is now consequently known as "the father of trigonometry."[3]
Sumerian astronomers introduced angle measure, using a division of...
...Trigonometry
 Introduction to trigonometryAs you see, the word itself refers to three angles  a reference to triangles. Trigonometry is primarily a branch of mathematics that deals with triangles, mostly right triangles. In particular the ratios and relationships between the triangle's sides and angles. It has two main ways of being used: 1. In geometryIn its geometry application, it is mainly used to solve triangles, usually right triangles. That is, given some angles and side lengths, we can find some or all the others. For example, in the figure below, knowing the height of the tree and the angle made when we look up at its top, we can calculate how far away it is (CB). (Using our full toolbox, we can actually calculate all three sides and all three angles of the right triangle ABC). 2. AnalyticallyIn a more advanced use, the trigonometric ratios such as as Sine and Tangent, are used as functions in equations and are manipulated using algebra. In this way, it has many engineering applications such as electronic circuits and mechanical engineering. In this analytical application, it deals with angles drawn on a coordinate plane, and can be used to analyze things like motion and waves. Chapter1Angles in the Quadrants( Some basic Concepts)In trigonometry, an angle is drawn in what is called the "standard position". The vertex of the angle is on the origin, and one side of the angle is fixed and drawn along...
...The Way Trigonometry is used in Astronomy
By: Joanna Matthews
Practical Applications of Advanced Mathematics
Mrs. Amy Goodrum
July 15, 2003
Abstract
This report is about how trigonometry is used in Astronomy. Even though trigonometry is applied in many areas, such as engineering, chemistry, surveying, and physics, it is mainly used in astronomy Trigonometry is used to find the distance of stars, the distance from one planet to another and from one plant to the sun. It is possible to find the radius of the Earth also. This report will basically give more insight in the way trigonometry and astronomy goes hand in hand.
Background
Trigonometry comes from a Greek word "trigonometria" put together from these 3 words: Tri (three) gonia (angle) metro (measure). Trigonometry has been around for many centuries, but in 140 BC a man named Hipparchus apparently wrote 12 books on the table of chords and became the founder of trigonometry. He was the first Greek mathematician to study triangular geometry. This study led him to write the 12 books.
Other people have added to Hipparchus’ work, but the two people that stands out the most are were Menelaus (ca. AD 100) and Ptolemy (ca. AD 100). Menelaus was a Greek mathematician that created six books on tables of chords. He created a couple of triangle properties. Menelaus had a big hand in spherical...
...Intro:
Trigonometry is a branch of mathematics that studies triangles and the relationships between their sides and the angles between these sides. The field evolved during the third century BC as a branch of geometry used extensively for astronomical studies. It is also the foundation of the practical art of surveying.
Trigonometry basics are often taught in school either as a separate course or as part of a precalculus course. Fields that usetrigonometry or trigonometric functions include Biology, Pharmacy, Chemistry, many Physical Sciences (Physics, Mechanics and Astronomy could have been developed without Trigonometry), Electrical Engineering, Mechanical Engineering, Civil Engineering, Architecture, Analysis on Financial Markets and electronics.
In this project you'll find out on how Angle of Depression and Angle of Elevation are measured. You'll get some ideas about Sum and Difference Identities.
I hope this could be a good reference of those topic mention and my their eyes be fed with satisfaction with the information.
Acknowledgement
In my field, IT (Information Technology) internet is a great source of reference in my homeworks, researches and projects; it helped me accomplish this project with the help of technology my works are more representable to read and more efficientlooking. I may want to recognized my Inspiration, in giving me some ideas and putting up the datas together to make...
...f ter
A Brief History of Trigonometry
A painting of the famous greek geometrist, and "father of measurement", Euclid. In the times of the greeks, trigonometry and geometry were important mathematical principles used in building, agriculture and education.
The Babylonians could measure angles, and are believed to have invented the division of the cirle into 360º.[1] However, it was the Greeks who are seen as the original pioneers of trigonometry.
A Greek mathematician, Euclid, who lived around 300 BC was an important figure in geometry and trigonometry. He is most renowned for Euclid's Elements, a very careful study in proving more complex geometric properties from simpler principles. Although there is some doubt about the originality of the concepts contained within Elements, there is no doubt that his works have been hugely influential in how we think about proofs and geometry today; indeed, it has been said that the Elements have "exercised an influence upon the human mind greater than that of any other work except the Bible.<Complete Dictionary of Scientific Biography, 2008>

[edit]First Tables of Sines or Cosines
Hiparchus
In the second century BC a Greek mathematician, Hipparchus, is thought to have been the first person to produce a table for solving a triangle's lengths and angles.[2]...
...Amongst the lay public of nonmathematicians and nonscientists, trigonometry is known chiefly for its application to measurement problems, yet is also often used in ways that are far more subtle, such as its place in the theory of music; still other uses are more technical, such as in number theory. The mathematical topics of Fourier series and Fourier transforms rely heavily on knowledge of trigonometric functions and find application in a number of areas, including statistics.
There is an enormous number of applications of trigonometry and trigonometric functions. For instance, the technique of triangulation is used in astronomy to measure the distance to nearby stars, in geography to measure distances between landmarks, and in satellite navigation systems. The sine and cosine functions are fundamental to the theory of periodic functions such as those that describe sound and light waves.
Fields which make use of trigonometry or trigonometric functions include astronomy (especially, for locating the apparent positions of celestial objects, in which spherical trigonometry is essential) 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...
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