Which of the following events occurred before the first appearance of the word "trigonometry" in print?
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Well let's look at the dates first\nA. 1538\nB. 1636\nC. 1802\nD. April 23, 1564\nE. January 4, 1643\nSources below in order of parts (so a is first)\nNow, the word trigonometry was first used in 1595 (last source), so the answer is a and d
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The history of maths or on a famous mathematician.
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Since ancient history regarding the concept.\n\nHistory of the notation:\n\nThe symbol "π" for Archimedes' constant was first introduced in 1706 by William Jones when he published A New Introduction to Mathematics, although the same symbol had been used earlier to indicate the circumference of a circle. The notation became standard after it was adopted by Leonhard Euler. In either case, 'π' is the first letter of περιφέρεια (periphereia, the Greek word for periphery) or περίμετρον (perimetron), meaning 'measure around' in Greek.
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Cosine, one of the six fundamental ratios of trigonometry. In any right triangle, the cosine of an acute angleA, usually written cos A, is defined as the ratio of the length of the side (that is not the hypotenuse) of the triangle that is adjacent to the angle, divided by the length of the hypotenuse of the triangle.
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http://en.wikipedia.org/wiki/History_of_mathematics\n\nis a good link.\n\nHere is some basic info: \n\nAlot stems from ancient egyptian and babylonian/mesopotamian folk where we see ideas of advanced counting, for example, fractions (egypt), land segregation in mesopotamia (fractional areas/percentages). base systems other than decimal (e.g. sexagesimal, base 60) were used frequently, and indeed today for example minutes in hours etc. The greeks developed much of the basis for what we use today, including much work on geometry, number theory and a more rigorous treatment of mathematical proof (e.g. euclid's elements is a very important book). there is alot after this, depends what you define as 'early history'. hope this is useful.
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Johann Castillon used the name cardioid for the first time, in a paper in the Philosophical Transactions of the Royal Society (1741).\n\nHowever, he was not the first person who used it.  For example, it was studied by Roemer (1674) in an investigation for the best form of gear teeth. \n\nCardioid is a special case of limacon of Pascal: a family of curves studied and named after Etienne Pascal (1588-1640), father of Blaise Pascal (1623-1662). \n\nI don't know whether they originally used polar co-ordinates which followed after the Cartesian system developed by Descartes in 1637. But given that the general formula for the limacon is a ± bcos(theta) or a ± bsin(theta), it's certainly possible.
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Johannes Gensfleisch zur Laden zum Gutenberg (c. 1398 – c. February 3, 1468) was a German metal-worker and inventor who achieved fame for his contributions to the technology of printing during 1447, including a type metal alloy and oil-based inks, a mould for casting type accurately, and a new kind of printing press based on presses used in wine-making. The exact origin of Gutenberg’s first presses is apparently unknown, and several authors cite his earliest presses as adaptations of heavier binding presses which were already in use. Tradition credits him with inventing movable type in Europe — an improvement on the block printing already in use there. By combining these elements into a production system, he allowed for the rapid printing of written materials, and an information explosion in Renaissance Europe. Yet, it must be noted that an iron printing press was first invented by Korea's Goryeo dynasty in 1234, 216 years ahead of Gutenberg's feat in 1450.
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You would think Pythagoras, but actually not originally.\nHe studied many years at the library of Alexandria (Ancient Egypt), whereupon he came upon this theorem (now named after him) first recorded by an ancient Egyptian mathematician known as (I think) Tet.\nSince it was not permitted to take things from the library, or even copy them he memorized it, then later taught it to his disciples as his own.
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First is the spelling.  It's trigonometry.\n\nSecond is the question.  You would need to be more specific.  There are many good online sources for that.  Just google it and search the sites.  There will be some university level sites or some simpler ones too.
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The use of grid lines on maps (latitude and longitude) was first suggested by the Greek astronomer Hipparcus about 300 years before Christ. He was the first who devised a method for fixing the location of places on earth by observation of the the sun, moon and stars. He worked out the mathematics of spherical trigonometry, which allowed the results of these observations to be plotted on an earth which he knew already to be a sphere.\n\nLatitude can be found easily by measuring the height of the sun at noon. The measurement of longitude is not so simple as you need an accurate clock.
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John Harrison developed longitude.\n\nLatitude is a bit more difficult to determine and is mostly about mathematics but I believe mathematician Karl Gauss had something to do with it. But you should research that some more.
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The basic idea behind trigonometry is that once you know the angles of a triangle, you'll know the ratios of the sides of the triangle.  And so if you know one side, you can use trig to find out the two other sides.\n\nSine, cosine, and tangent deal with right triangles.  They tell you the ratios of different pairs of sides in the right triangle.\n\nHere's a brief intro:\nhttp://opera.answers.com/trigonometry
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Well maths is the foundation of most ares of science, especially physics, and physics relates to many jobs in fields like engineering etc. Trigonometry in maths at first seems to just relate to triangles, but apart from finding unknown sides and angles, it has many applications. the relationship between the sides of a triangle, in terms of sine, cosine and tangent apply to many areas of physics. You may have heard of trig graphs, and in physics, you can see how many things like waves, simple harmonic motion and AC current all relate to trigonometrical concepts, that is, looking at objects in motion in terms of a reference circle
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I  do not believe mathematics existed before man. Mathematics was created by man to assist him in discovering the universe and the world we live in.\n\nIt is true that pi, the ratio of the circumference of a circle to its diameter, may have existed before man, as could many other constants that man has discovered such as e. But man invented mathematics. It was not out there all the time for us to find.\n\nMathematics is used constantly in  Newtonian Physics and Modern Physics. Many of the formulas were developed empirically by observing events over and over and then theorizing a formula to predict and or explain the phenomena being observed. This is why mathematics explains physical laws so well. But man is constantly creating new and refining old laws as he continues to try and explain the world we live in. \n\nMathematics pre-existed mankind? Balderdash.
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The value of π has been known in some form since antiquity. As early as the 19th century BC, Babylonian mathematicians were using π=25/8, which is within 0.5% of the exact value.\n\nThe Egyptian scribe Ahmes wrote the oldest known text to give an approximate value for π, citing a Middle Kingdom papyrus, corresponding to a value of 256 divided by 81 or 3.160.\n\nIt is sometimes claimed that the Bible states that π=3, based on a passage in 1 Kings 7:23 giving measurements for a round basin as having a 10 cubit diameter and a 30 cubit circumference. Rabbi Nehemiah explained this by the diameter being from outside to outside while the circumference was the inner brim; but it may suffice that the measurements are given in round numbers. Also, the basin may not have been exactly circular.\n\nThe Chinese mathematician Liu Hui computed π to 3.141014 (good to three decimal places) in AD 263 and suggested that 3.14 was a good approximation.\n\nThe Indian mathematician and astronomer Aryabhata in the 5th century gave the approximation π = 62832/20000 = 3.1416, correct when rounded off to four decimal places.\n\nThe Chinese mathematician and astronomer Zu Chongzhi computed π to be between 3.1415926 and 3.1415927 and gave two approximations of π, 355/113 and 22/7, in the 5th century.\n\nThe Indian mathematician and astronomer Madhava of Sangamagrama in the 14th century computed the value of π after tranforming the power series expansion of π/4 into the form\n\nπ = √12(1 - 1/(33) + 1/(532) - 1/(733) + ... \nand using the first 21 terms of this series to compute a rational approximation of π correct to 11 decimal places as 3.14159265359. By adding a remainder term to the original power series of π/4, he was able to compute π to an accuracy of 13 decimal places.\n\nThe Persian Muslim mathematician and astronomer Ghyath ad-din Jamshid Kashani (1350-1439) correctly computed π to 9 digits in the base of 60, which is equivalent to 16 decimal digits as:\n\n2 π = 6.2831853071795865 \nThe German mathematician Ludolph van Ceulen in 1615 computed the first 32 decimal places of π. He was so proud of this accomplishment that he had them inscribed on his tombstone.\n\nIn 1789, the Slovene mathematician Jurij Vega improved John Machin's formula from 1706 and calculated the first 140 decimal places for π of which the first 126 were correct [1] and held the world record for 52 years until 1841, when William Rutherford calculated 208 decimal places of which the first 152 were correct.\n\nThe English amateur mathematician William Shanks, a man of independent means, spent over 20 years calculating π to 707 decimal places (accomplished in 1873). In 1944, D. F. Ferguson found (with the aid of a mechanical desk calculator) that Shanks had made a mistake in the 528th decimal place, and that all succeeding digits were fallacious.
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It was Pythagoras who was the first to question the flat earth theory, although probably just the most famous....incidently it was considered heracy at the time.
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There is actually a little controversy surrounding whether or not Pythagoras was actually the one who discovered the theorem, or if it was another of his associates, the Pythagoreans.  This website: http://www.geom.uiuc.edu/~demo5337/Group3/hist.html has some interesting history of other cultures illustrating an understanding of this, without expressing it in literal mathematical language.\n\nAs far as your second question, a great illustration can be found at http://mathforum.org/library/drmath/view/53937.html    The pythagorean theorem is actually a specific instance of the law of cosines, which is represented as a^2 = b^2 + c^2 - 2ab*cos(a).  As you can see, the equation only becomes the pythagorean theorem if 2ab*cos(a) = 0, which only happens if the angle is 90 degrees.