The Father of Trigonometry - 3474 Words

The first trigonometric table was apparently compiled by Hipparchus, who is now consequently known as the father of trigonometry.[3] Sumerian astronomers introduced angle measure, using a division of circles into 360 degrees.[4]They and their successors 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. The ancient Nubians used a similar methodology.[5] The ancient Greeks transformed trigonometry into an ordered science.[6] Classical Greek mathematicians (such as Euclid and Archimedes) studied the properties of chordsand inscribed angles in circles, and proved theorems that are†¦show more content†¦Many English speakers find it easy to remember what sides of the right triangle are equal to sine, cosine, or tangent, by memorizing the word SOH-CAH-TOA (see below under Mnemonics). The reciprocals of these functions are named the cosecant (csc or cosec), secant (sec), and cotangent (cot), respectively: The inverse functions are called the arcsine, arccosine, and arctangent, respectively. There are arithmetic relations between these functions, which are known as trigonometric identities. The cosine, cotangent, and cosecant are so named because they are respectively the sine, tangent, and secant of the complementary angle abbreviated to co-. With these functions one can answer virtually all questions about arbitrary triangles by using the law of sines and the law of cosines. These laws can be used to compute the remaining angles and sides of any triangle as soon as two sides and their included angle or two angles and a side or three sides are known. These laws are useful in all branches of geometry, since every polygon may be described as a finite combination of triangles. [edit]Extending the definitions Fig. 1a - Sine and cosine of an angle ÃŽ ¸ defined using the unit circle. The above definitions apply to angles between 0 and 90 degrees (0 and Ï€/2 radians) only. Using the unit circle, one can extend them to all positive and negative arguments (seetrigonometric function). The trigonometric functions are periodic, with aShow MoreRelatedHistory of Trigonometry4574 Words   |  19 PagesRunning Head: History of Trigonometry History of Trigonometry Rome Fiedler History of Mathematics 501 University of Akron April 29, 2012 History of Trigonometry: An Introduction Trigonometry is useful in our world. By exploring where these concepts come from provides an understanding in putting this mathematics to use. The term Trigonometry comes from the Greek word trigon, meaning triangle and the Greek word meatria meaning measurement. However itRead MoreGeorg Ferdinand, Philipp Cantor857 Words   |  4 PagesGeorg Ferdinand Ludwig Philipp Cantor was born on March 3, 1845 in Saint Petersburg, Russia. His father, Georg Waldemar Cantor, was a successful merchant working as a wholesaling agent, then later found another job as a broker in the St. Petersburg Stock Exchange. Georg’s father was born in Denmark and had a deep passion for culture and arts. His mother, Maria Anna Bà ¶hm, was from Russia and very musical. Georg inherited his love for music and arts from his parents, considering he was a wonderfulRead MoreAnnual Islamic Symposium On The Arts And Sciences1042 Words   |  5 Pageswide reaching field has some of the most practical use s today and that all came from these arab mathematicians. Trigonometry is the branch of math dealing with angles and triangles and it is important to surveyors and astronomers. Trigonometry was mostly developed by Al-Battani an astronomer and mathematician who created tables giving ratios of the sides of right triangles. Trigonometry was developed in the tenth century within which the functions of sine, cosine, tangent, cotangent, secant, and cosecantRead More Leonhard Euler Essay672 Words   |  3 Pages Leonhard Euler Euler made large bounds in modern analytic geometry and trigonometry. He made decisive and formative contributions to geometry, calculus and number theory. Born: 15 April 1707 in Basel, Switzerland Died: 18 Sept 1783 in St Petersburg, Russia Introduction Eulers father wanted his son to follow him into the church and sent him to the University of Basel to prepare for the ministry. However geometry soon became his favourite subject. Euler obtained his fathers consentRead MoreShort Story925 Words   |  4 Pagessecond time as he looked at his son strangely. â€Å"Oh, um†¦ I-I—† Phillip stuttered. â€Å"The trigonometry help, dear,† Krista stated. â€Å"Did everything go alright? Did you get back on track in your class?† â€Å"Um, yes, I guess it all went alright,† answered Phillip, â€Å"but, I’m still going to need to stay after for probably the rest of the week to get completely caught up.† â€Å"You’re that far behind?† asked Krista. â€Å"Trigonometry is hard!† â€Å"Alright, alright,† Krista backpedaled a bit defensively. â€Å"You can take asRead MoreThe Importance Of A Few College General Education Courses1070 Words   |  5 Pageswrite research papers. Teachers and those who work in education also need sharp writing skills. Like medical professionals, those working in education must be able to write up reports on their students. For my mother, a speech pathologist, and my father, a guidance counselor, writing is a big part of their everyday life. A large part of their job is writing about the progress of the students they see. Teachers must also know how to teach their students how to properly write papers so they themselvesRead MoreAll The Light We Can Not See By Anthony Doerr1514 Words   |  7 PagesMarie-Laure was a blind French girl who lived in Paris with her father, who was one of the only people who treated her as a normal person and considered her disability an obstacle she could be able to conquer. He helped her dev elop skills to manage her condition in various ways such as making her wooden models of their neighborhood to be able to navigate the streets, and teaching her braille. Marie-Laure was very dependent on her father and his assistance, and when they moved to Saint-Malo where heRead MoreEssay on Film Review of Dead Poets Society642 Words   |  3 PagesPerry discovers that his real passion in life is acting and proceeds to land the role of Puck in a Midsummer Nights Dream at the local theater. He begins to weave a tangled web of deception by failing to inform his father, then lying to Mr. Keating when his father finds out and demands he quit the play. Feeling trapped, after his final performance and a standing ovation, he takes his own life. The most important discovery made in the film was by Todd Anderson. Todd isRead MoreA Swedish Born Diplomat973 Words   |  4 Pageshave both coped with panic attacks and social anxiety respectively. My father lives with a moderate form of OCD, while my younger brother lives with a more severe form of Autism. Although my immediate family does not identify concurrently as one religion, my sister and I identify as Methodist, while our parents and younger brother either are undecided. However, my father’s parents were brought up Catholic, and had sent my father to a Catholic high school. First and foremost, I firmly believe in theRead MoreEssay on My Love for Learning576 Words   |  3 Pageshelped me realize how important education is and how much freedom and opportunity education would grant me. They would tell me stories about their life in the former Soviet Union and how hard it was for them to persevere in the communist regime. My father, specifically, would talk about anti – Semitism in the Soviet Union and the difficulty he had to get a degree in Medicine because of the governmental quota system that limited the number of Jews entering academia. He would talk about his fear of

College Physics - 6022 Words

Wilson, College Physics, 6th Edition Chapter 9 Exercises MC = Multiple Choice Question, CQ = Conceptual Question, and IE = Integrated Exercise. Throughout the text, many exercise sections will include â€Å"paired† exercises. These exercise pairs, identified with red numbers, are intended to assist you in problem solving and learning. In a pair, the first exercise (even numbered) is worked out in the Study Guide so that you can consult it should you need assistance in solving it. The second exercise (odd numbered) is similar in nature, and its answer is given at the back of the book. 9.1 Solids and Elastic Moduli Use as many significant figures as you need to show small changes. 1. MC The pressure on an elastic body is described by†¦show more content†¦(d) 26. MC For the pressure–depth relationship for a fluid [pic] it is assumed that (a) the pressure decreases with depth, (b) a pressure difference depends on the reference point, (c) the fluid density is constant, (d) the relationship applies only to liquids. (c) 27. MC When measuring automobile tire pressure, what type of pressure is this: (a) gauge, (b) absolute, (c) relative, or (d) all of the preceding? (a) 28. CQ (Figure 9.27 shows a famous â€Å"bed of nails† trick. The woman lies on a bed of nails with a cinder block on her chest. A person hits the anvil with a sledgehammer. The nails do not pierce the woman’s skin. Explain why. see ISM 29. CQ Automobile tires are inflated to about [pic] whereas thin bicycle tires are inflated to 90 to [pic]—at least three times as much pressure! Why? see ISM 30. CQ (a) Why is blood pressure usually measured at the arm? (b) Suppose the pressure reading were taken on the calf of the leg of a standing person. Would there be a difference, in principle? Explain. see ISM 31. CQ (a) Two dams form artificial lakes of equal depth. However, one lake backs up 15 km behind the dam, and the other backs up 50 km behind. What effect does the difference in length have on the pressures on the dams? (b) Dams are usually thicker at the bottom. Why? see ISM 32. CQ Water towers (storage tanks) are generallyShow MoreRelatedA Student Survey of Mechanics Test Data870 Words   |  4 PagesData for Introductory Physics Courses (A Research Journal Critique) In partial fulfillment of the requirements in Physics 501: Theoretical Mechanics during the First Semester of the school year 2008 – 2009 Maria Jocelyn T. Claridad Master of Arts in Science Education with Specialization in Physics Prof. Antriman V. Orleans October, 2008 Interactive-Engagement vs. Traditional Methods: A Six Thousand-Student Survey of Mechanics Test Data for Introductory Physics Courses Richard R. 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The Bubonic Plague (Black Death) Free Essays

The pandemic of the bubonic plague swept across Europe in 1347 and spread to England in 1348. It is known today as the Black Death. During these years, the plague affected the lives of people all across England and killed over half of England’s population. We will write a custom essay sample on The Bubonic Plague (Black Death) or any similar topic only for you Order Now It’s impact was enormous, not only because of the rapid decrease in the population but because of the pessimism, fear and suspicion. â€Å"Plague is a deadly infectious disease that is caused by the enterobacteria, Yersinia pestis. Primarily carried by rodents (most notably rats) and spread to humans via fleas† – Wikipedia The plague caused a huge decline in England’s population. It killed over 5 million people (70% of the population) Some of the first symptoms were vomiting, giddiness, headaches, shivering, tongue turns white, and intolerance to light. Some of the later symptoms are pains in the joints, breaking blood vessels, internal bleeding, and skin turning black (the result of the dried blood from internal bleeding) During the plague peasants left their jobs because they were afraid they would get the Black Death and die. Many also left for other villages to find new jobs, better wages and conditions. Since there wasn’t many farmers to make food, the price of food went up during the plague. There were not enough people to look after animals and crops, so they died too. Some people in urban areas died, not from Bubonic Plague but from starvation. Some villages became completely abandoned because of the villagers evacuating. Because of the Black Plague villages faced starvation. Town and cities faced food shortages as the villages that surrounded them could not provide them with enough food. A big consequence of the Black Death was inflation – the price of food went up creating more labour for the poor. In some parts of England, food prices went up by four times. Many Lords were short of desperately needed labour for the land that they owned. After the Black Death, Lords encouraged peasant to leave their villages and come work for them. When peasants did this, the Lord refused to let them return to their original village. The peasants started demanding higher wages as they knew that the Lord was desperate to get his harvest. The Black Death brought great depression that was felt through out England and affected the lives of millions, it is one of the most lethal disease out breaks in history. How to cite The Bubonic Plague (Black Death), Papers