Trigonometry in Astronomy | TRIGONOMETRY IN THE "REAL WORLD"
Astronomy was the driving force behind advancements in trigonometry. a certain relation to one another do not everywhere show the same relation between the For his astronomical work Hipparchus needed a table of trigonometric ratios. Trigonometry is a branch of mathematics that studies relationships involving lengths and angles of triangles. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies. The 3rd -century astronomers first noted that the lengths of the sides of a. Using trigonometry in astronomy has allowed us to calculate the distance to nearby stars through parallax. Parallax is, “The effect whereby the position or.
I am currently enrolled in a Trigonometry class.
My teacher has asked us to write a paper on how trigonometry affects my life and careers. I have spent hours researching this and I have found that trigonometry has affected astronomy as well as many other professions but once I read over the information it does not ever tell me how.
The websites and such simply tell me formulas which are complicated and I don't understand their meanings and uses. So my question to you is, how is astronomy influenced or impacted by trigonometry? Is it greatly used and if so to find what? I would greatly appreciate it if you would reply to my question quickly. Thank you very much in advance for your reply and time.
Probably the biggest impact that trigonometry has had in Astronomy is in the finding of distances to nearby stars through the method of parallax. As you know, the Earth orbits around the Sun once a year. This means that at six month intervals the Earth is looking at a star from the two corners of an isosceles triangle where the point is at the star.
He wrote a six-book treatise on chords, which was mentioned by Theon of Alexandria, but those books have all been lost. Heath His only surviving work is a three-book work called Sphaerica, whose third book contains some excellent information about the development of trigonometry and is the earliest surviving work on spherical trigonometry.
Unfortunately the Greek version of this text is lost, and all that remains is an Arabic version translated a thousand years after the original was written.
To make matters worse, various translators over the years have had their commentary included in the work, and it becomes difficult to separate the original from the commentators. Nevertheless, this work still provides a good source for the development of Greek trigonometry.
How is trigonometry used in astronomy?
In the first book of the Sphaerica, there is the first known conception and definition of a spherical triangle Heath Menelaus describes a spherical triangle as the area included by arcs of great circles on the surface of a sphere subject to the restriction that each of the sides or legs of the triangle is an arc less then a semicircle.
He then goes on to give the main propositions about spherical triangles corresponding to Euclid's propositions about plane triangles. The second book has astronomical interest only. The third book contains trigonometric ratios. The first proposition in the third book is Menelaus's theorem with reference to a spherical triangle and any transversal great circle cutting the sides of a triangle.
R ather than using a spherical triangle he expresses his proposition in terms of two intersecting great circles.
All the arcs are less than a semicircle. He then goes on to prove which is Menelaus's theorem for spherical trigonometry.
In Menelaus' proof he distinguished three or four separate cases. Below is a diagram of Menelaus's theorem for plane trigonometry: The rest of the third book consists of trigonometric propositions that were necessary for astronomical work. The last great contributor to trigonometry in the Greek period is Ptolomy.
Very little is known about Ptolemy's actual life. He made astronomical observations from Alexandria in Egypt during the years AD The first observation which we can date ex actly was made by Ptolemy on 26 March while the last was made on 2 February There is no evidence that Ptolemy was anywhere other than Alexandria.
Heath says "it is evident that no part of the trigonometry, or of the matter preliminary to it, in Ptolemy was new. What he did was to abstract from earlier treatises, and to condense into the smallest possible space, the minimum of propositions necessary to establish the methods and formulas used. It is difficult to tell what additions and modifications Ptolemy made to already existing works.
Toomer calls the Almagest a masterpiece of clarity and method, superior to any ancient scientific textbook and with few peers from any period.
Trigonometry - Wikipedia
But it is much more than that. Far from being a mere compilation of earlier Greek astronomy, as it is sometimes described, it is in many respects an original work. Whatever the case, Ptolemy's Almagest is our main source of information on Hipparchus and on Alexandrian trigonometry. The early copyists must have felt that the Almagest rendered previous writings obsolete and superfluous.PreCalculus - Trigonometry: The Right Triangle (22 of 26) Distance to Near-By Star = ?
The use of the Sine, cosine, and tangent functions lay several hundred years in the future. However, the table of chords can be used in formulas that are equivalent to present day formulas for the trigonometric functions. The table of chords in the Alma gest is likely the same as Hipparchus' table or an expansion of it but we cannot be sure since we don't have a copy of Hipparchus' table to compare it with.