Essay on Six Trig Functions

Essay on Six Trig Functions Essay on Six Trig Functions THE SIX TRIGONOMETRY FUNCTIONS BY: Chambria Rogers & Marc TRIGONMETRIC RATIO The six trigonometric functions are traditionally defined in terms of the six ratios of the sides of a right triangle. This approach is valid for positive angles of measure smaller than 90∘. Consider a right triangle ââ€" ³ABC with the angle C being the 90∘ angle. There are six functions that are the core of trigonometry. There are three primary ones that you need to understand completely: Sine (sin) Cosine (cos) Tangent (tan) The other three are not used as often and can be derived from the three primary functions. Because they can easily be derived, calculators and spreadsheets do not usually have them. Secant (sec) Cosecant (csc) Cotangent (cot) Sine (SIN) FUNCTION The law of sines for plane triangles was known to Ptolemy and by the tenth century Abu'l Wefa had clearly expounded the spherical law of sines. It seems that the term "law of sines" was applied sometime near 1850 In a right triangle, the sine of an angle is the length of the opposite side divided by the length of the hypotenuse. The sine function has a number of properties that result from it being periodic and odd. The Law of Sines relates various sides and angles of an arbitrary (not necessarily right) triangle: sin(A)/a = sin(B)/b = sin(C)/c = 2r. where A, B, and C are the angles opposite sides a, b, and c respectively. Furthermore, r is the radius of the circle circumscribed in that triangle. COSINE In a right triangle, the cosine of an angle is: The length of the adjacent side divided by the length of the hypotenuse. The law of cosines is best thought of as an extension of the Pythagorean Theorem, with a term that adjusts if the included angle is not a right angle. The usual statement of the theorem is descibed in terms of sides a, b, and c; and opposite angles A, B, and C. The usual expression is c2=a2+b2-2abCos(C). The theorem is cyclic about any of the three sides and so it can also be expressed in the alternate forms a2=b2+c2-2bcCos(A) and b2=a2+c2-2acCos(B). Since the cosine of a right angle is zero, each of the equations reduces to the usual form of the Pythagorean Theorem when the associated angle is 90o. TANGENT statement about the relationship between the tangents of two angles of a triangle and the

Law of Business Transactions assignment Essay Example | Topics and Well Written Essays - 2000 words

Law of Business Transactions assignment - Essay Example nited Floors Ltd had included an exclusion clause in its contract, which required intimation of any alleged defects within three weeks of fitting the carpets. As such, it had included a clause, whereby its liability per contract was to be restricted to five hundred pounds. Peter is seeking refund of the two, thousand, three hundred pounds paid by him and compensation for the business lost, during the time the carpet was being replaced. United Floors Ltd refuses to accept and relies on its exclusion clause. An exclusion clause can be enforced by resorting to adhesion contracts or standard form contracts. The party which draws up such contracts offers negligible choice to the other party to the contract. In the words of Downes, an authority on contract law, wherever, there is great disparity in the bargaining power of the parties to the contract, exclusion clauses can prove to be extremely prejudicial.1 Legislation like the Unfair Contract Terms Act 1977 or UCTA and the Unfair Terms of the Consumer Contract Regulations 1999 or UTCCR have been enacted, in order to exercise stringent control on the use of exclusion clauses. The UCTA makes a business liable for not fulfilling obligations or duties that are consequent to what has been done or is to be done in the normal course of business2. Peter’s contract with the United Floors Ltd is subject to the UCTA, because consumer contracts fall under its purview3. In contractual terms reasonableness is of paramount importance and the UCTA verifies as to whether an exclusion clause, after taking into consideration the circumstances that should have normally been known to the contracting parties, is rational4. In this manner the UCTA grants wide discretion to the courts, in determining whether an exclusion clause is reasonable or not. If a contracting party wishes to take recourse to an exclusion clause in the contract, then the onus of establishing its reasonableness rests on it5. The UTCCR deals with all the contractual

Greek Civilization Essay Example | Topics and Well Written Essays - 1500 words

Greek Civilization - Essay Example The roles which have been assigned to men and women are natural and that they should live by them. It is imperative that whatever roles that exist between a man and a wife, they are not to be substituted; this is because various adaptations have been given to either of them so that they can be able to perform the assigned responsibilities. In making a man and a wife, God did it with the intention that there will be the concept of one party giving and the other party receiving. For instance, a wife was made with little ability for outdoor activities, instead, she was given the will and knowledge for indoor activities, these include housekeeping, the nurturing of new born babies and a great affection for the new born and the family at large. For the wife to be comfortable, the man provides security in the home, he has been given the ability to provide courage to the wife. All these things work well where sharing is done. When these two parties stick to their various roles, there is bound to be ultimate success. Ischomachus became a great wealthy farmer because he was able to train his wife to manage house chores, rule and train slaves. This made him concentrate on managing those activities that were more outdoor and hence succeeded. In a definite case, it needs to be that way. When a man and a wife concentrate in the areas of their expertise, they often excel. For instance, in his conversation with his wife, Ischomachus points that a shelter is very important for people, they should have a cover on their heads. Unfortunately, as soon as these things have been done, new needs will always come again, hence the need for one who will constantly do it, who in this case is the man. Ischomachus notes that the couple ought to procreate. The man and the wife grow old and at one point in time, their efforts need to be complemented. Having children gives them a chance to

Marcel Duchamps Fountain and the Dadaist Movement Essay Example for Free

Marcel Duchamps Fountain and the Dadaist Movement Essay This is a paper about the Dadaist movement and a work of art that is very representative of Dadaist philosophy: Fountain by Marcel Duchamp. The Fountain is one of the most controversial works of art ever. Many argued at the time that it could not be considered art. At first glance, it began as away to test the integrity of an art societys rules for how and what it would consider to be a work of art. It is more complex than this as will be shown. The controversy it raised also forced a re-assessment of the definition â€Å"art. † It embodied the Dada movements irreverence for the rules of a society that had gone mad. To understand Fountain in relation to the Dadaist movement, we must first understand Dadaism and why it emerged as a movement in the early 20th century. The history of Fountain and its creator will be told. Finally, these individual parts of the story will be assembled to give a complete picture of the significance of Fountain as work of modern art The First World War removed any glamorous or noble image of war that may have remained from the days before the mechanization and streamlining of the weapons of war. The death and suffering brought about the Great War had a great effect on soldiers and civilians alike. The number of people killed and wounded was terrible enough. It was the great numbers killed coupled with the lack of a reasonable explanation for sending young men to die or to lose a leg, or an eye, or an arm that perturbed the fragile psychological balance that virtually drove an entire society to the precipice of madness. Death permeated every aspect of life-like never before. Many questioned how a supposedly rational society could destroy itself in such a violent and irrational manner. A movement composed of artists, performers, and intellectuals called for a rejection of the social and artistic norms of the civilization that had brought about the horrors of WWI. The senseless killing proved that life was without meaning; at least it had no meaning for the architects of their world. The movement called for a new beginning that would bring meaning to life. The name of this movement was Dada. There are several explanations for the name. One is that â€Å"da-da† is a common first word said by babies (Adams 915).. â€Å"Dada† is also the French term for a wooden rocking horse. These references to young children symbolize the new beginning that the Dada movement called for in their manifesto (Adams914). Although Dada was a response to a grim situation, one of its characteristics was a lighthearted attitude. From this playful premise, another rationale for the name can be derived from the Slavic â€Å"da, da! † which of course means â€Å"yes, yes† (Adams 914). Yet another rumor claims it was taken from a randomly opened page of a French-German dictionary with the word â€Å"dada† in it. Perhaps the name has no meaning and it was just an arbitrary choice by some of the founding members. This explanation fits perfectly with the â€Å"anti-art† philosophy of Dada. They wished to shock the public into recognizing the absurdity of the Western world through their art (Frank 398). Jean Arp, a French artist, poet, and founding member of Dada summarized the movement with this: While the thunder of guns rolled in the distance, we sang, painted, glued, and composed for all our worth. We are seeking an art that would heal mankind from the madness of the age (qtd. In Frank 398). Artist Marcel Janco said: Dada was not a school of artists, but an alarm signal against declining values, routine and speculation, a desperate appeal on behalf of all forms of art, for a creative basis on which to build a new and universal consciousness of art (qtd. In Frank 397). They wished to remedy society in a way that was in direct opposition to the malevolence of war and destruction. They would heal society through benevolent art that was fun and creative. Fountain (1917) by Marcel Duchamp embodies much of the Dada movements irreverence for all traditional aesthetic values. It has an interesting story behind it. Duchamp was one of many artists that immigrated to New York from war-ravaged Europe. He was at the center of a controversy concerning one of his earlier paintings titled Nude Descending a Staircase in 1912. The painting is akin to time-lapse photograph of a nude woman walking down a staircase with each step superimposed on each other. It give the strong impression of movement; movement being a popular subject of interest by artists of the time. Duchamp was asked to remove the painting before it was to be exhibited at an exposition in France because the organizers of the show felt it was too â€Å"radical† and the public was not ready for such a painting (Camfield 20). Duchamp complied, but was dismayed at being the victim of censorship by an organization that professed to honor democratic ideals in their charter. This is important because this group, the French Independants, would soon have an American counterpart known as the American Independents Society. Duchamp never forgot the hypocrisy of being censored by the French Independants and when the American Independents Society was formed, he wished to test the fortitude of the democratic ideals it too claimed to cherish. The Independents founding principle was â€Å"no jury, no prize† (Camfield 22). This principle would, in theory, allow for a broad interpretation for what could be considered art and spur the great creativity in the creation of art by the Societys members. Submissions by artists that were to be displayed at expositions should have been accepted without being screened and possibly censored by a â€Å"jury† of any kind. Duchamp would submit, under a pseudonym, the work titled Fountain. The reason Duchamp chose to submit such an outrageous piece was not mainly to test the democratic principles of the Independents. Duchamp saw it as a way to inject a true work of Dada into the public view with the purpose of shocking them into recognizing the folly of Western civilization, a key aim of the Dadaist movement. Duchamp was known for the slight additions drawn or painted onto everyday objects or mass-produced replicas of famous art pieces and named them â€Å"Ready-Mades. † Duchamp combined his playful personality and sharp wit with his Ready-Mades. One of his famous Ready-Mades is L. H. O. O. Q. , a revised Mona Lisa in which he has added a mustache to the familiar face of La Gioconda originally painted by da Vinci 500 years ago. The title is meant to be phonetically the same as the word â€Å"look. † The letters are also an acronym in French standing for â€Å"She has a hot ass. † These demonstrates that Duchamps intent was to shock the observer while at the same time doing this with a good sense of humor. One of the greatest shocks the world was to ever receive from a work of art would be administered by Duchamps Fountain. To test the democratic strength of the Independents as discussed earlier, Duchamp submitted a porcelain urinal he purchased from a plumbing store shortly before the first exposition of the American Society of Independent Artists. The urinal was to be displayed upside down from its intended position, the name R. Mutt was inscribed on it, and it was christened with the title Fountain. It arrived a few days before the beginning of the show and it was judged by the â€Å"jury† that was not supposed to exist according to one of the founding principles of the Independents. Just as Nude Descending a Staircase was snubbed from being viewed a few years previous, Fountain too suffered the same indignity of being censored. Duchamp immediately resigned as a director of the American Independents in protest. It was not known until later that R. Mutt was really Duchamp. Fountain is significant in the context of the Dada movement because it was the opposite of anything that Western culture would dream of considering art. That was exactly the point of the movement when it began in Zurich, Switzerland as a response to the horrors of the mechanized death machine unleashed by the First World War. It also asked an important question: â€Å"What is Art? † Duchamp thought that the subjects of his Ready-Mades are as artistic the subjects chosen by a photographer because they are both about the choice of subject matter made by the artist. Photography was well established as an art form in Duchamps time. Why is his choice of subject matter any different from what the photographer chooses to capture on film? The only difference between a Ready-Made and a photograph is the medium in which the subject resides. Why Duchamp chose what he did to create Fountain is hard to discern from the contradictory statements made over the years until his death in 1968. William Camfield makes a good argument that Duchamp did not pick out the urinal at random as he sometimes implied in some responses to questions he was asked about any aesthetic considerations he took when the urinal was purchased. Camfield says: Turning from those late interviews back to 1917 and Duchamps work that preceded Fountain, we find not aesthetic indifference but an oeuvre of extraordinary visual and intellectual rigor. And Fountain fits in that oeuvre. Far from being the product of an impulsive decision to challenge the principles of the Independents, Fountain seems to be expressive of its creator, related to other work by Duchamp, and reflective of other art and the culture around him. (43) It makes sense that the style and creativity exhibited by Duchamp in the other works of art he created around the time of Fountain would be evident in a work that was much more than a last-minute random selection. Fountain seems to be very consistent with his other works during this period and casts doubt on the idea that he did it for anything less than to espouse the tenets of Dada; beliefs he was strongly committed to. Works Cited Adams Laurie S. , Art Across Time. New York: McGraw-Hill, 2002 Camfield, William A. , Marcel Duchamp Fountain. Houston, Texas: Houston Fine Art Press, 1989 Cubitt, Sean. â€Å"Marcel Duchamp† Leonardo 35 (2002): 99-100 de la Croix, H. and Tansey, Richard G. , Art Through the Ages. New York: HBJ, 1975 Frank, Patrick, Artforms. New Jersey: Pearson, 2006 Goldsmith, Steven. â€Å"The Ready-Mades of Marcel Duchamp: The Ambiguities of an Aesthetic Revolution. † The Journal of Aesthetics and Art Criticism 42 (1983) 197-208 Molesworth, Helen. â€Å"The Everyday Life of Marcel Duchamps Ready-Mades† Art Journal 57 (1998): 50-61

Comparing and Contrasting Society in the Book, The Lathe of Heaven and

Comparing and Contrasting Society in the Book, The Lathe of Heaven and the Movie, Matrix In the book The Lathe of Heaven, by Ursula K. Le Guin, there are many similarities and some differences in society in comparison to the movie Matrix. The two stories settings take place in different locations. Although, throughout both stories many huge changes are made, the people in the societies remain unaware of the changes. Then, similarly, only a certain few individuals are knowledgeable of the true reality. A difference between The Lathe of Heaven and the Matrix is the place setting. The Lathe of Heaven's characters are in the real world. The real world is physical and tangible, filled with items that tiger senses. People have feelings and react differently to situations. Each one depending on the person and the circumstance. The real world is the truth, the truth is reality. Although, this reality is changed with one night's dream, from George Orr. Orr is a man who has the ability to change truth, including history and every humans view of what reality is. When Orr dreams, h is thoughts become reality. With one dream he changes today, and the history. Orr is the only one who is aware of the original, true reality. In the Matrix, however, what the society believes to be the real world, is really a computer program invented and run by Machines. In the Matrix, Machines have taken over the human population and created a world, known as the Matrix. This world is only lived out through the minds of the people, as the people are kept in holding tanks. The world, or Matrix is a computer program, and only known to be a computer program by the Machines and a few selected individuals. Similarly, in The Lathe of Heaven and in the Matrix ... ...er begins to manipulate his dreams, abusing his ability to change reality. Orr decides to inform a lawyer, Heather Lelache, with hope she will aid in preventing Orrs dreaming. Together the three of them are the only ones aware of the dreams, and therefore the only ones knowledgeable of the original truth, true reality. In both stories, the novel, The Lathe of Heaven, and the movie, Matrix, the societies compare and contrast. The stores share in similar themes and plot but have different aspect to the changes made in society. The changes in society both, positively and negatively affect and influence the people. Included are powers that are overbearing and controlling that need to be stopped, such as the Machines and the dreaming. Similarly, both stories involve people who want to change the world for themselves and ones who prefer to allow God to plan the future.

Reflective Essay on Students with Disabilities

In a presentation about parents and families of students with disabilities, the Riley family came up and shared their experiences about living with Catherine, a woman who has Down syndrome. The three presenters who shared were Molly, Nola, and Catherine. Molly, who is Catherine’s older sister, talked about what it was like growing up together with Catherine and how it affected her life. Nola, Catherine’s mother, told what it was like bringing and raising a child with Down syndrome in this world. Catherine also shared a bit about her life and how she has been successful despite having a disability.Molly and Catherine are sisters who spent their childhood growing up together. With Molly being only sixteen months older than Catherine, they were very close. They even shared a room together for eighteen years of their life. Molly always made sure that her and Catherine had the typical sister relationship growing up. They did everything together and had the same friends. Cath erine was expected to fit in with everyone, and not be given excuses. Molly was always a competitive sister which had Catherine constantly working to get an edge.This relationship between Molly and Catherine not only strengthened the bond, but also helped the family. With Molly helping Catherine achieve a normal life, this helped Nola out as a mother. Nola a mother of three children, who worked as a teacher for thirty-five years, always had her hands full. She was never too shy to ask people for help, with regard to Catherine, that provided help, guidance, and support. With physical therapy Catherine was able to learn the things that her sister Molly and brother John were able to do. Besides that, Nola said that the three kids lived a normal life and all grew up just fine.Nola learned and taught her family to be patient, help each other, to take pleasure in their 3 accomplishments, to encourage each other, to have fun, and to truly be a family. Being a teacher gave Nola an advantage as she always fought for anything that would benefit Catherine in her education. Nola had Catherine put into speech therapy which made a great difference in Catherine’s life, as she can now speak clearly with little difficulty. Everything Nola did for Catherine was to benefit her in anyway and help keep her leading as normal of a life as possible.Catherine went above and beyond that as she has excelled in many aspects of her life. Catherine has spent her whole life with Down syndrome yet did not let it slow her down and affect how she lived her life. Her family never held her back or kept her from doing the things she wanted to do. Her sister always had that tough love for Catherine which always forced Catherine to do better and develop just like any normal sibling would. She always had the support of her family while still being independent, which allowed her to grow and develop into who she is today.Catherine has been leading a successful life, doing many things even the a verage woman her age would not be doing. She is employed as an elementary inclusion aid in the Hazelton Area School District where she has worked since graduating there in 1995. Catherine has belonged to a gym for fifteen years where she does things like cardio, kickboxing, and circuit training exercises. She always strives to eat healthy and maintain a good diet. Her hobbies include poetry, journaling, aerobics, computer, travel, reading, and dancing. Catherine belongs to a local church where she helps out at church functions and serves on the parish.All of these activities and things Catherine does in her life help her not only achieve normalcy 4 in life but success. Her life is probably more active and outgoing than most people her age which makes it even more of an accomplishment for Catherine. I personally was inspired by this presentation and thought it was a real eye opener. I have gone through life thinking people with Down syndrome can not achieve the same things that peopl e without a disability can and that’s just not true. Catherine has proved that she can do anything she wants and can lead a normal life just like anyone else.In fact she probably is more active and outgoing than most women her age are. Also I thought that the presentation really showed that people with disabilities need to be given every opportunity, if not more, to help them succeed in life. Society should not hold them back or limit them just because they have a disability. People with disabilities can lead a normal and great life just like everyone else. This is proved by Catherine, who has developed into the woman she is today, a successful, loving, and friendly woman who just happens to have a disability.

Cry the Beloved Country dialectical journal - 1678 Words

Cry, the Beloved Country Dialectical Journals Theme: Racial Inequality Injustice Quote Response â€Å"Kumalo climbed into the carriage for non-Europeans, already full of the humbler people of his race†¦Ã¢â‚¬  (43) How there’s a carriage exclusively for non-Europeans is understandable at the time period that this novel is set in, but people who read this in the 21st century might think that this is odd how Europeans couldn’t stand to ride in the same carriage as non-Europeans. â€Å"Black and white it says, black and white, though it is red and green. It is too much to understand.† (47) The order it goes, black and white then red and green. It shows you that the whites are more superior because they are the sign to go, and the blacks have to stop and†¦show more content†¦And being in a foreign place makes it even more confusing on if you should trust anyone or not. When you’re poor like Kumalo was, money was very precious to you. He was taking money that was going to be used for clothes. Seeing someone run off with your money is something that makes you lose faith in the human race. Cry, the Beloved Country Dialectical Journals Theme: Economic Prosperity v. Loss of Values Quote Response â€Å"She came here to look for her husband who was recruited for the mines†¦ She lives in Claremont, not far from here. It is one of the worst places in Johannesburg†¦ †¦ that is her work, she makes and sells it†¦ These women sleep with any man for their price†¦ She has been in prison, more than once.† (53) Kumalo’s sister went to the big city to find her husband and it turns out that she never did. At least that’s what it seems like it’s trying to hint at. It seems like as soon as she entered a place to be rumored as a better economic area, she lost all morals and values. This is sad really, for both Kumalo and his sister. (55) Cry, the Beloved Country Dialectical Journals Theme: Poverty Quote Response â€Å"How can I use it? he said. This money was to send Absalom to St. Chad’s†¦ This money we have saved for that purpose will never be used for it.† (38-39) Stephen feels if he were to use the money they saved for his son it wouldn’t be right. He also knows that ifShow MoreRelatedCry, The Beloved Country Journal1487 Words   |  6 Pages Jeffrey Dao Ms. Hastings Period 1 October 7, 2014 Cry, the Beloved Country Journal Table of Content Topic Page Number Focus on Conflict Responses 2 Focus on Theme Responses 3-5 SAR Responses Chapter Questions Responses Dialectical Journals Works Cited  Focus on Conflict In book 1 of Cry, the Beloved Country, the main conflict was Kumalo’s loss of faith. In this quote,â€Å"But that he should kill a man, a white man! There was nothing that he could remember, nothing, nothing at all, that couldRead MoreOrgan Donation1872 Words   |  8 Pagestransplants because of the shortage of donated organs (Medline Plus). The detrimental outcome upon U.S. citizens due to low organ donation is immense compared to that of Austria, France and Spain. Austria has the shortest organ waiting list of the world’s countries, with twenty-nine donors per one million inhabitants, whereas America has six donors per one million inhabitants (Donate Life America). These severe statistics prompt the question, why is the rate of organ donation in the United States, seeminglyRead Morewisdom,humor and faith19596 Words   |  79 Pagesâ€Å"people are wise to the extent that they use their intelligence to seek a common good. They do so by balancing, in their course s of action, their own interests with those of others and those of larger entities, like their school, their community, their country, even God.† In fostering wisdom, Sternberg also thinks it is important to teach people to see â€Å"things from others’ perspectives as well as one’s own,† to tolerate â€Å"other people’s points of view, whether or not one agrees with such views.† He refers