Free Essays on Chinas Battle On Overpopulation

CHINA’S OVERPOPULATION BATTLE China’s population policy, more commonly referred to as the One Child Policy, is one of the most controversial topics in the world, and the only one of its kind in history. It has been praised and criticized by many, and the world has yet to see what results it will have in the long run. The debatable one child policy of China has ultimately changed the views and stirred the emotions of many people on how to solve the population problem. The Chinese government has taken the enforcement of family planning and birthright laws to an extreme by violating the civil rights of its citizens, which has adversely affected the morale of its people. China implemented a one-child per family policy in 1979 in order to address the issue of unchecked population growth in a country with limited resources. While this policy was not enforced until 1979, population control actually began in the late fifties. This policy says all families are limited to one child unless that child is unable to work or dies. Only then are they allowed to have a second child without having to pay additional taxes on that child. Although China’s family planning efforts have dropped the population growth from 1970’s 33.43 percent per 1000 to 15.23 percent in 1999, abuse, forced abortions, and sterilization, and in some cases, even murder are the cause of what Chinese officials hail as a success. Many women have stated that they have been forced to have abortions due to declined applications for birth certificates. Some of these abortions are done just days before the mothers due date. There are also many women who tell of forced sterilization even after complying with the policy because they were accused of trying to hide their pregnancy. Destruction of property, including the destruction of entire homes, Are common among families who choose to disobey these laws. I am shocked and appalled at what I have read on the overpo... Free Essays on Chinas Battle On Overpopulation Free Essays on Chinas Battle On Overpopulation CHINA’S OVERPOPULATION BATTLE China’s population policy, more commonly referred to as the One Child Policy, is one of the most controversial topics in the world, and the only one of its kind in history. It has been praised and criticized by many, and the world has yet to see what results it will have in the long run. The debatable one child policy of China has ultimately changed the views and stirred the emotions of many people on how to solve the population problem. The Chinese government has taken the enforcement of family planning and birthright laws to an extreme by violating the civil rights of its citizens, which has adversely affected the morale of its people. China implemented a one-child per family policy in 1979 in order to address the issue of unchecked population growth in a country with limited resources. While this policy was not enforced until 1979, population control actually began in the late fifties. This policy says all families are limited to one child unless that child is unable to work or dies. Only then are they allowed to have a second child without having to pay additional taxes on that child. Although China’s family planning efforts have dropped the population growth from 1970’s 33.43 percent per 1000 to 15.23 percent in 1999, abuse, forced abortions, and sterilization, and in some cases, even murder are the cause of what Chinese officials hail as a success. Many women have stated that they have been forced to have abortions due to declined applications for birth certificates. Some of these abortions are done just days before the mothers due date. There are also many women who tell of forced sterilization even after complying with the policy because they were accused of trying to hide their pregnancy. Destruction of property, including the destruction of entire homes, Are common among families who choose to disobey these laws. I am shocked and appalled at what I have read on the overpo...

Blowing The Gaff

Blowing The Gaff Blowing The Gaff Blowing The Gaff By Sharon I recently mentioned a book called Mind The Gaffe, which is all about errors in English. It got me to thinking about the word gaffe and other related expressions. I set out to do some digging in my trusty dictionary and came up with a few surprises. The word gaffe means a social blunder and originates from French in the 19th century. It should not be confused with the word gaff, which has a variety of interesting meanings. If you fish, then you probably use a sturdy pole with a strong hook to capture the biggest catch of your life. Thats called a gaff, and youll need it if you want to avoid tales about the one that got away. If you actually manage to land that fish, then gaff becomes a verb that shows how you hook it. Sailors know a gaff as a special boom to which a gaffsail is attached. Cockfighting is a favored pastime in some parts of the world, and in that context, gaff describes the spur thats attached to a gamecocks leg. Gaff is also a popular slang word with several meanings. It can mean nonsense talk, cheat or hoax. If youre British and you blow the gaff, then you reveal a secret, while Americans and Canadians who stand the gaff are able to take a bit of ribbing. Gaff was also an old British term for someones home, as well as a cheap theater or music hall in Victorian times. Want to improve your English in five minutes a day? Get a subscription and start receiving our writing tips and exercises daily! Keep learning! Browse the Expressions category, check our popular posts, or choose a related post below:Arrive To vs. Arrive At8 Proofreading Tips And TechniquesInspiring vs. Inspirational

Keeping a Client Coursework Example | Topics and Well Written Essays - 250 words

Keeping a Client - Coursework Example Black and that her particular situations will be negotiated in the upcoming months and tailored to her needs (Carrell & Heavrin, 2008). b) I would react to Ms. White’s demand for limiting my time at the site, by presenting to her the amount of work to be covered through the process of negotiation to closing. By letting her know the contents, maybe contained in agreement template in favor of Mr. Black and the time it took through that negotiation, she should appreciate the time needed. c) Ms. White apparent problem here is the fact that she could be facing opposition from establishing a retailer shop. First step is to identify her problem, verify it alongside defining this problem and analyze. After proper analysis has been conducted, then the last process before implementing is to identify an alternative which can have a better outcome than what we have already identified. If the alternative is better, then it means we have to shift to the alternative, but if it is of less value then we have to implement the first option (Carrell & Heavrin, 2008). d) Ms. White has already had a pre-conception about what we are supposed to negotiate hence it might be had to get her out of the situation. But to avoid this situation, I will have to frame her issues differently to her specific needs that are different from that of Mr. Black. I should be able to frame in terms of gains she should be benefitting from particular and unique to her preferred site (Education, 2014). e) As mentioned in (d) above, the benefit is our goal, in comparison to the barriers along the way. The best technique, therefore, in closing this deal with Ms. White is by using problem-solving mediation approach. A conflict is already in existence between us, a problem too exists, due to incompatibility of our interests. So we will assess the conflict and define the differences. In our case, the problem is opposition to her location whiles our conflict, too, is her apparent position of

Big brother assignment Example | Topics and Well Written Essays - 250 words - 1

Big brother - Assignment Example related to the technology advancement shows that the Americans are being monitored by the companies, and big businesses are through keeping phone-call records, tracking their cars and through the colored printed copies one can get from a shop or office, which is without people’s knowledge and is unethical as these data mining companies do not inform people before hatching their information and data through different sources and later they may use it for making justice acts or planning something hurtful for the person. Such situations become abusive and offending for people who are unaware of their daily life being on record by someone. 3. Even when it comes to protecting one’s information from data-mining and surveillance industries, through the information-technology security one should know that no system is foolproof. One should limit access of any sensitive information, use strong passwords, change and update them regularly. Keeping financial information private would help in a way. These things should be considered while talking on the phone or

Frederick C Hamilton Essay Example for Free

Frederick C Hamilton Essay The architectural sculptured layout of the Fredrick C Hamilton building is on display at Denver Art Museum. The actual building, named after the CEO of the Petroleum company is near completion. Frederick C Hamilton post modern style designed building is a dome, shell shaped architect, comparable to the Sydney Opera House. (http://en. wikipedia. org/wiki/Architecture) The outside Hamilton building structure is designed using patterns from the expressionism art era. The post modern design is very simplistic, without many intricate details. Anyone viewing the attractive building would be curiously drawn to the building. The Frederick C Hamilton building serves as the main entrance to popular culture and art areas. It is the only dome shaped building in the area, surrounded by buildings with pattern designs from the Renaissance and Romantic art eras. Once inside the building, the person feels transported in totally different planet. The glass ceilings, and skylights allows the sun to shine through, into the building. The creative designed structures portrays a very pleasant atmosphere to everyone entering it. (http://www. designbuild-network. com/projects/dam/) The designer of this coned, alien shaped 350,000 sq ft building is Daniel Libeskined, whom also designed the World Trade Center after the attack. The Frederick C Hamilton building will hold nearly one thousand parking spaces. The construction materials used for the building are titanium, steel, and concrete. The creativity behind the amazing designs centering around romantic style buildings requires real genius imagination.

Open Fields :: Descriptive Memories Essays Papers

Open Fields When I think back to the days when I was a child, I think about all of my wonderful childhood memories. Often I wish to go back, back to that point in life when everything seemed simpler. Sometimes I think about it too much, knowing I cannot return. Yet, there is still one place I can count on to bring me back to that state of mind, my grandparents' house. There is something to be said about lying on one's back in an open field hour upon hour, staring up at a vast, blue sky. With no one around and not another house for miles, it is a great place to be alone, to listen. In the country, I can pick up all the wonderful sounds of nature commonly lost amidst the bustle of the city. The wind speaks as it blows across the land, whistling through the trees. Crickets rub their wings in song for anyone to hear. An unseen friend scurries beneath the fallen leaves, as an owl above questions who is there. Heading back towards the house, I soak in all the beauty of the surrounding landscape. There are towering groves of trees, creek beds lined with wildflowers emitting delightful fragrances, and sunsets that astound. Still, I walk cautiously. For all of nature’s beauty, trouble can still take form out here, whether it is running into a slithering snake or stumbling across a prickly thistle. Looking further into the distance, I spot the horses gracefully galloping along, their sleek manes dancing across their powerful bodies. As I pass the pond, I skip a stone across the water and I think about all the "real" stories the pond could tell of the ones that got away. Along side its banks I hear a familiar sound, as the bullfrogs' bellows lead the way for nightfall. The night will bring the cool country air, and with it the thick aroma of the wood-burning stoves. On some evenings, if I am lucky enough, some warm apple-butter jam may even be waiting for me back at the house. Now that I am older, I look for changes. I have grown to expect them. My grandparents will soon be gone, but the memories of the land they live on and I grew up on will always be with me.

One Cannot Escape Big Brother Essay

In 1984, by George Orwell, society is portrayed as having lost all traces of individuality, creative thought, and love and humanity. This â€Å"Negative Utopia† depicts the possibility of the future despair of the human race whilst warning readers of the dangers of totalitarianism. The overlying mood in 1984 is the bleakness of the future of the human race. The main character though, Winston Smith, is caught in this society that is dedicated to conformity with a mind full of intelligence, individuality, and rebellious thoughts. Winston is targeted by the government from the beginning because of his continual thoughtcrime as well as his rebellious actions with Julia. However, in a society as bleak and desolate as Orwell has depicted, Winston’s actions against the Party and Big Brother were essentially futile. Throughout the novel, Winston believes that though society forces him to conform on the outside, he can still fight the system with his thoughts and by being with Julia in secret. He believes that his own individuality reveals that there is at least a small sliver of hope for humanity, but this is not so. Syme even questions Winston, â€Å"How could you have a slogan like ‘freedom is slavery’ when the concept of freedom has been abolished?† (pg.47). There is so much moral decay within the Party, Winston is wasting his breath and energy by trying to bring down Big Brother; it is too great, and he is too small, despite how intelligent he may be. In Orwell’s fiction society, there is no hope, no potential light for the future. Society is too far gone, as shown through aspects of life such as telescreens, Hate Week, the Hate Song, and Newspeak. The government has molded the people of Oceania’s minds into the ideal citizen: unfeeling, lacking any creative thought, love, or uniqueness. The citizens who slip by and do possess these qualities will be vaporized at some point and Winston knows this throughout the novel. Yet he still believes that in some way, he may be of help to the Brotherhood, even though he is not even sure of its existence. One thing that separated the government of 1984 from any modern day government is that when someone was a traitor, or made some attempt to overthrow the government, they were not punished, but rather â€Å"cured†. In the novel, O’Brian, who is a symbol Big Brother, states, â€Å"We are not content with negative obedience, nor even with the most abject submission. When finally you surrender to us, it must be of your own free will. We do not destroy the heretic because he resists us: so long as he resists us we never destroy him. We convert him, we capture his inner mind, we reshape him. We burn all evil and all illusion out of him; we bring him over to our side, not in appearance, but genuinely, heart and soul. We make him one of ourselves before we kill him.† (pg. 318) This portrays how Big Brother essentially ensures its own success by turning their enemies into supporters of their cause rather than persecuting them. Winston had no chance to take down Big Brother because when he was caught, he would not even become a legacy, or a shining light for others to follow suit; he would become nonexistent, a changed man who would be taught to love Big Brother. By not voicing his true opinions about the Party, Winston would have continued to know the truth behind it. However, because he did, O’Brian and other Party members â€Å"cured† him, and molded his mind into what they wished it to be. By going against Big Brother, Winston became a clay mold of the ideal fascist citizen. Winston had no chance of being happy in the world set by Orwell. He was too intelligent to go through life without questioning Big Brother, and the irony exists in the fact that that was ultimately his intellectual demise. However, if Winston had just lived in acceptance of the fact that society was so horribly corrupt, and turned away from the atrocities of civilization, he would have been much better off. He would not have been tortured, he would not have had to experience the betrayal of O’Brian, and he would not have gained then lost Julia. In today’s world, it is perhaps better to have loved and lost; but in Orwell’s 1984, one never truly gained anything because Big Brother was always watching. Orwell says in the novel, â€Å"If you want a picture of the future, imagine a boot stamping on a human face—forever† (pg 271). No amount of rebellion could possibly stop this metaphorical boot from crushing humanity. Winston could have saved himself from a lifetime of even more hurt and despair if he had just kept to himself and turned away from the evils of Big Brother. After all, the slogan â€Å"Big Brother is watching you† (pg 2) was not just a saying for the people of Oceania: it was a sad truth. Thus, Winston would have been much more fortunate given the circumstances if he had not gone against the Party.

Infrastructure

Is infrastructure a key factor to the growth and stability of the economy? or is it a non-factor and needs not to be maintained and improved to better serve and help improve the economy. Infrastructure in general is the system of transport and communication in a state, region or country. A famous Canadian geographer was once quoted saying, â€Å"†¦ any region which has a well-developed transportation and communication network also enjoys a high degree of economic prosperity†¦ This statement has sparked much controversy between geographers, Politicians, as well as conomists. Question is, is there a link between a well-developed infrastructure and economy prosperity (economy growth)? Without a doubt, there is a direct link. Infrastructure facilitates the basic functions of a society that are necessary to transport resources and people, produce and trade goods, provide essential services and ultimately reduce poverty.The direct link can be understood better by looking at the effects of infrastructure. The drawbacks of poor infrastructure lead to high transport cost especially in landlocked areas, thus the economy gets affected. Employment is low where there is poor infrastructure. Lack of adequate infrastructure perpetuates poverty, because it denies possibilities. Affordability, it is relatively expensive to maintain and build.Due to this factors and the analyses from the department of treasury know is an ideal time to increase our investment because, infrastructure investments have long-term economic benefits and create Jobs in the short run, there is currently a high level of underutilized resources that can be used to improve and expand our infrastructure. The cost of transportation is lowered for American households, there is a strong demand by the public and businesses for dditional transport infrastructure capacity.Long-term economic benefits from infrastructure create Jobs in the short run and this is a crucial and important aspect of growth and economic stability in a country. As much as the infrastructure is important and maintaining it being so expensive, if the economy is not good it is hard to have a developed and well maintained infrastructure system. Research has shown that well-designed infrastructure investments can raise economic growth, productivity, and land values, while also providing significant spillovers to areas such as energy efficiency, public health and manufacturing.Thus to say both infrastructure and economy go hand in hand. They affect each other both negatively and positively. On June 29, 1956 President Dwight Eisenhower signed the federal-Aid Highway Act of 1956 â€Å"The national system of interstate and defense highways† according to Eisenhower the purpose of this was to eliminate unsafe roads, inefficient routes, traffic Jams and all of the other things that got in the way of â€Å"speedy, safe transcontinental travel. † for all these reasons the 1956 law declared that the constru ction of an elaborate expressway system was essential to the national interest and growth of the economy.Todays Interstate System is what our suburban lifestyle and caused the vast proliferation of businesses from HoJos to Holiday Inns. And if you order something online, most likely it's a truck barreling along an interstate that gets the product to your door. there are a lot of undiscovered materials that we could use not only that we have all the man power and technology we need to build whatever we need to improve our infrastructure Among those who gain employment as a result of additional infrastructure investment, the average unemployment rate has averaged approximately 13 percent over the past 12 months.This is more than one and one- half times the current national unemployment rate. Within the construction sector, which accounts for the majority of direct employment resulting from infrastructure investment, the unemployment rate has averaged 15. 6 percent over the past 12 mon ths. Construction costs and other costs associated with building projects are especially low in the current environment. As a result, the President has taken decisive action to accelerate project permitting and environmental review.In the President's August 31, 2011, memorandum, he directed the heads of all executive epartments and agencies to: (1) identify and work to expedite permitting and environmental reviews for high-priority infrastructure projects with significant potential for Job creation; and (2) implement new measures designed to improve accountability, transparency, and efficiency through the use of modern information technology.Relevant agencies should monitor the progress of priority projects; coordinate and resolve issues arising during permitting and environmental review; and develop best practices for expediting these decisions that may be instituted on a ider scale, consistent with applicable law. In addition, in this year's State of the Union address, the Preside nt announced his intention to â€Å"sign an executive order clearing away the red tape that slows down too many construction projects. † Investing in transportation infrastructure creates middleclass Jobs.Analysis suggests that 61 percent of the Jobs directly created by investing in infrastructure would be in the construction sector, 12 percent would be in the manufacturing sector, and 7 percent would be in the retail and wholesale trade sectors, for a total of 80 percent in hese three sectors. Nearly 90 percent of the Jobs in these three sectors most affected by infrastructure spending are middleclass Jobs, defined as those paying between the 25th and 75th percentile of the national distribution of wages.The President's proposal emphasizes transportation choices, including mass transit and high-speed rail, to deliver the greatest long-term benefits to those who need it most: middle-class families. The average American family spends more than $7,600 a year on transportation, which is more than they spend on food and twice what they spend n out-of-pocket health care costs. For 90 percent of Americans, transportation costs absorb one out of every seven dollars of income. This burden is due in large and this calls for better infrastructure and investing more in it to make progress.Multi-modal transportation investments are critical to making sure that American families can travel without wasting time and money stuck in traffic. A more efficient transportation money. Traffic congestion on our roads results in 1. 9 billion gallons of gas wasted per year, and costs drivers over $100 billion in wasted fuel and lost time. More efficient ir traffic control systems would save 3 billion gallons of Jet fuel a year, translating into lower costs for consumers.Finally, new research indicates that Americans who were able to live in housing were able to save $200 per month in lower costs over the past decade. Americans want more transportation investment. After years of underinvestment in our transportation system, Americans' satisfaction with our public transit system s middling when compared to public satisfaction with highways and public transit systems around the world. the Global competitiveness report for 2012-13, published arlier this month by the world economic forum showed that U.S infrastructure was ranked 7th in 2008, but has dropped to 14 in the world this year. The U. S. score dropped from 6. 10 in 2008 to 5. 7 this year (7 is the top score, and 1 is the worst score). One of the main reasons for the deterioration of U. S. infrastructure in the last five years, a deterioration which is reflected in the drop in ranking, is the economic downturn which began in 2008. Funding for roads, bridges, highways, and other critical infrastructure is largely dependent on state revenues, and as states ook less money in, they were forced to spend less on infrastructure maintenance and improvements.Passing the MAP-21 bill was an accomplishment for a d o-little Congress, but serious issues about how to pay for transportation in the future have yet to be resolved. The recent highway bill, MAP-21 replaces SAFETEA-LU, the last long-term federal transportation bill, which expired in 2009 for example, it did not increase spending on transportation, even though lawmakers were aware of the need to do so. The 2009 stimulus package did help shore up some infrastructure, but was not nearly sufficient to meet the countrys needs.

Sensuality Versus Heroism essays

Sensuality Versus Heroism essays In the early 15th century, artist Donatello sculpted a male nude in bronze, David, using Classical ideals. At the end of the 15th century this sculpture was interpreted by another artist, Andrea Del Verrocchio. While both sculptures portray David standing over the head of Goliath, this is where the similarities end. These two versions of the biblical subject are much different in the way David is portrayed, his attire, as well as the overall feeling invoked from the two sculptures. Verrocchio and Donatello both show David standing over the head of the slain Goliath. Donatello's David portrays him as a sensual figure rather than a hero. His sword is pointed downward by his side, and his gaze too is also downward. This makes it look as if he is humble about his victory. Verrocchio's David, on the other hand, portrays him as a hero, valiantly standing over the head of Goliath. His sword is pointed outward r rather than down, making it look as if he is still ready to battle. His gaze is also up and he The two artist's differences in attire on both sculptures also differs. Donatello leaves his sculpture of David nude except for a hat and boots. The articles of clothing are hardly noticeable due to the fact that they are a soft and appealing. Verrochio's David, however, is clothed in attire suitable for battle. His garment seems to be that of a warrior The overall feeling invoked from both sculptures is the last difference between the two. Donatello's David invokes a feeling of sensuality and elegance in not only the way David is posed, but also in his serene facial features. Verrochio's David, in contrast, invokes a feeling of heroism as well as childlike undertones. His features are more boyish Donatello's use of attire, the way David is portrayed, as well as the sen ...

The 36 Trig Identities You Need to Know

The 36 Trig Identities You Need to Know SAT / ACT Prep Online Guides and Tips If you’re taking a geometry or trigonometry class, one of the topics you’ll study are trigonometric identities. There are numerous trig identities, some of which are key for you to know, and others that you’ll use rarely or never. This guide explains the trig identities you should have memorized as well as others you should be aware of. We also explain what trig identities are and how you can verify trig identities. In math, an "identity" is an equation that is always true, every single time. Trig identities are trigonometry equations that are always true, and they’re often used to solve trigonometry and geometry problems and understand various mathematical properties. Knowing key trig identities helps you remember and understand important mathematical principles and solve numerous math problems. The 25Most Important Trig Identities Below are six categories of trig identities that you’ll be seeing often. Each of these is a key trig identity and should be memorized. It seems like a lot at first, but once you start studying them you’ll see that many follow patterns that make them easier to remember. Basic Identities These identities define the six trig functions. $$sin(ÃŽ ¸) = 1/{csc(ÃŽ ¸)}$$ $$cos(ÃŽ ¸) = 1/{sec(ÃŽ ¸)}$$ $$tan(ÃŽ ¸) = 1/{cot(ÃŽ ¸)} = {sin(ÃŽ ¸)}/{cos(ÃŽ ¸)}$$ $$csc(ÃŽ ¸) = 1/{sin(ÃŽ ¸)}$$ $$sec(ÃŽ ¸) = 1/{cos(ÃŽ ¸)}$$ $$cot(ÃŽ ¸) = 1/{tan(ÃŽ ¸)} = {cos(ÃŽ ¸)}/{sin(ÃŽ ¸)}$$ Pythagorean Identities These identities are the trigonometric proof of the Pythagorean theorem (that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides, or $a^2 + b^2 = c^2$). The first equation below is the most important one to know, and you’ll see it often when using trig identities. $$sin^2(ÃŽ ¸) + cos^2(ÃŽ ¸) = 1$$ $$tan^2(ÃŽ ¸) + 1 = sec^2(ÃŽ ¸)$$ $$1 + cot^2(ÃŽ ¸) = csc^2(ÃŽ ¸)$$ Co-function Identities Each of the trig functions equals its co-function evaluated at the complementary angle. $$sin(ÃŽ ¸) = cos({Ï€/2} - ÃŽ ¸)$$ $$cos(ÃŽ ¸) = sin({Ï€/2} - ÃŽ ¸)$$ $$tan(ÃŽ ¸) = cot({Ï€/2} - ÃŽ ¸)$$ $$cot(ÃŽ ¸) = tan({Ï€/2} - ÃŽ ¸)$$ $$csc(ÃŽ ¸) = sec({Ï€/2} - ÃŽ ¸)$$ $$sec(ÃŽ ¸) = csc({Ï€/2} - ÃŽ ¸)$$ Negative Angle Identities Sine, tangent, cotangent, and cosecant are odd functions (symmetric about the origin). Cosine and secant are even functions (symmetric about the y-axis). $$sin(-ÃŽ ¸) = -sin(ÃŽ ¸)$$ $$cos(-ÃŽ ¸) = cos(ÃŽ ¸)$$ $$tan(-ÃŽ ¸) = -tan(ÃŽ ¸)$$ Sum and Difference Identities These are sometimes known as Ptolemy’s Identities as he’s the one who first proved them. $$sin(ÃŽ ± + ÃŽ ²) = sin(ÃŽ ±)cos(ÃŽ ²) + cos(ÃŽ ±)sin(ÃŽ ²)$$ $$sin(ÃŽ ± – ÃŽ ²) = sin(ÃŽ ±)cos(ÃŽ ²) – cos(ÃŽ ±)sin(ÃŽ ²)$$ $$cos(ÃŽ ± + ÃŽ ²) = cos(ÃŽ ±)cos(ÃŽ ²) – sin(ÃŽ ±)sin(ÃŽ ²)$$ $$cos(ÃŽ ± – ÃŽ ²) = cos(ÃŽ ±)cos(ÃŽ ²) + sin(ÃŽ ±)sin(ÃŽ ²)$$ Double-Angle Identities You only need to memorize one of the double-angle identities for cosine. The other two can be derived from the Pythagorean theorem by using the identity $sin^2(ÃŽ ¸) + cos^2(ÃŽ ¸) = 1$ to convert one cosine identity to the others. $$sin(2ÃŽ ¸) = 2 sin(ÃŽ ¸) cos(ÃŽ ¸)$$ $$cos(2ÃŽ ¸) = cos^2(ÃŽ ¸) – sin^2(ÃŽ ¸) = 1 – 2 sin^2(ÃŽ ¸) = 2 cos^2(ÃŽ ¸) – 1$$ $$tan(2ÃŽ ¸)={2 tan(ÃŽ ¸)}/{1– tan^2(ÃŽ ¸)}$$ Additional Trig Identities These three categories of trig identities are used less often. You should look through them to make sure you understand them, but they typically don’t need to be memorized. Half-Angle Identities These are inversions of the double-angle identities. $$sin2(ÃŽ ¸) = {1/2}(1-cos (2ÃŽ ¸))$$ $$cos2(ÃŽ ¸) = {1/2}(1+ cos (2ÃŽ ¸))$$ $$tan2(ÃŽ ¸) = {1-cos(2ÃŽ ¸)}/{1+ cos (2ÃŽ ¸)}$$ Sum Identities These trig identities make it possible for you to change a sum or difference of sines or cosines into a product of sines and cosines. $$sin(ÃŽ ±) + sin(ÃŽ ²)= 2sin({ÃŽ ± + ÃŽ ²}/ 2) cos({ÃŽ ± - ÃŽ ²}/ 2)$$ $$sin(ÃŽ ±) - sin(ÃŽ ²)= 2cos({ÃŽ ± + ÃŽ ²}/ 2) sin({ÃŽ ± - ÃŽ ²}/ 2)$$ $$cos(ÃŽ ±) + cos(ÃŽ ²)= 2cos({ÃŽ ± + ÃŽ ²} / 2) cos({ÃŽ ± - ÃŽ ²}/ 2)$$ $$cos(ÃŽ ±) - cos(ÃŽ ²)= -2sin ({ÃŽ ± + ÃŽ ²}/ 2) sin({ÃŽ ± - ÃŽ ²}/ 2)$$ Product Identities This group of trig identities allows you to change a product of sines or cosines into a product or difference of sines and cosines. $$sin(ÃŽ ±) cos(ÃŽ ²)= {1/2}(sin (ÃŽ ± + ÃŽ ²) + sin (ÃŽ ± - ÃŽ ²))$$ $$cos(ÃŽ ±) sin(ÃŽ ²)= {1/2}(sin (ÃŽ ± + ÃŽ ²) - sin (ÃŽ ± - ÃŽ ²))$$ $$sin(ÃŽ ±) sin(ÃŽ ²)= {1/2}(cos (ÃŽ ± - ÃŽ ²) - cos(ÃŽ ± + ÃŽ ²))$$ $$cos(ÃŽ ±) cos(ÃŽ ²)= {1/2}(cos (ÃŽ ± - ÃŽ ²) + cos(ÃŽ ± + ÃŽ ²))$$ Verifying Trigonometric Identities Once you have gone over all the key trig identities in your math class, the next step will be verifying them. Verifying trig identities means making two sides of a given equation identical to each other in order to prove that it is true. You’ll use trig identities to alter one or both sides of the equation until they’re the same. Verifying trig identities can require lots of different math techniques, including FOIL, distribution, substitutions, and conjugations. Each equation will require different techniques, but there are a few tips to keep in mind when verifying trigonometric identities. #1: Start With the Harder Side Despite what you may initially want to do, we recommend starting with the side of the equation that looks messier or more difficult.Complicated-looking equations often give you more possibilities to try out than simpler equations, so start with the trickier side so you have more options. #2: Remember That You Can Change Both Sides You don’t need to stick to only changing one side of the equation. If you get stuck on one side, you can switch over to the other side and begin changing it as well. Neither side of the equation needs to be the same as how it was originally; as long as both sides of the equation end up being identical, the identity has been verified. #3: Turn all the Functions Into Sines and Cosines Most students learning trig identities feel most comfortable with sines and cosines because those are the trig functions they see the most. Make things easier on yourself by converting all the functions to sines and cosines! Example 1 Verify the identity $cos(ÃŽ ¸)sec(ÃŽ ¸) = 1$ Let’s change that secant to a cosine. Using basic identities, we know $sec(ÃŽ ¸) = 1/{cos(ÃŽ ¸)}$. That gives us: $$cos(ÃŽ ¸) (1/{cos(ÃŽ ¸)}) = 1$$ The cosines on the left cancel each other out, leaving us with $1=1$. Identity verified! Example 2 Verify the identity $1 − cos(2ÃŽ ¸) = tan(ÃŽ ¸) sin(2ÃŽ ¸)$ Let’s start with the left side since it has more going on. Using basic trig identities, we know tan(ÃŽ ¸) can be converted to sin(ÃŽ ¸)/ cos(ÃŽ ¸), which makes everything sines and cosines. $$1 − cos(2ÃŽ ¸) = ({sin(ÃŽ ¸)}/{cos(ÃŽ ¸)}) sin(2ÃŽ ¸)$$ Distribute the right side of the equation: $$1 − cos(2ÃŽ ¸) = 2sin^2(ÃŽ ¸)$$ There are no more obvious steps we can take to transform the right side of the equation, so let’s move to the left side. We can use the Pythagorean identity to convert $cos(2ÃŽ ¸)$ to $1 - 2sin^2(ÃŽ ¸)$ $$1 - (1 - 2sin^2(ÃŽ ¸)) = 2sin^2(ÃŽ ¸)$$ Now work out the left side of the equation $$2sin^2(ÃŽ ¸) = 2sin^2(ÃŽ ¸)$$ The two sides are identical, so the identity has been verified! Example 3 Verify the identity $sec(-ÃŽ ¸) = sec(ÃŽ ¸)$ The left side of the equation is a bit more complicated, so let’s change that secant into a sine or cosine. From the basic trig identities, we know that $sec(ÃŽ ¸) = 1/{cos(ÃŽ ¸)}$, which means that $sec(-ÃŽ ¸) = 1/{cos(-ÃŽ ¸)}$. Substitute that for the left side: $$1/{cos(-ÃŽ ¸)} = sec(ÃŽ ¸)$$ The negative angle identities tell us that $cos(-ÃŽ ¸) = cos(ÃŽ ¸)$, so sub that: $$1/{cos(ÃŽ ¸)} = sec(ÃŽ ¸)$$ Again, we know that $sec(ÃŽ ¸) = 1/{cos(ÃŽ ¸)}$, so we end up with: $$sec(ÃŽ ¸) = sec(ÃŽ ¸)$$ Identity verified! Summary: Trig Identities Solver You’ll need to have key trig identities memorized in order to do well in your geometry or trigonometry classes. While there may seem to be a lot of trigonometric identities, many follow a similar pattern, and not all need to be memorized. When verifying trig identities, keep the following three tips in mind: Start with the trickier side Remember that you can change both sides of the equation Turn the functions into sines and cosines What's Next? Wondering which math classes to take in high school? Learn the best math classes for high school students to take by reading our guide! Wondering whether you should take AB or BC Calculus? Our guide lays out the differences between the two classesand explains who should take each course. Interested in math competitions like the International Math Olympiad? See our guide for passing the qualifying tests.

The Black Arts Movement Essay Example | Topics and Well Written Essays - 750 words

The Black Arts Movement - Essay Example Rising of the Moon, To Kill a Mockingbird, Ice Age and Jazz are examples of modern protest literature, which vehemently protest against social injustices, ethnic biased ness and gender discrimination. Thus, protest literature aims to shield and proclaim the human rights bestowed upon man from Almighty God without discrimination. The violation of human rights on biased grounds is emphatically condemned by the protest writers, dramatists and poets. The literature, protecting the rights of African Americans and highlighting their miseries, while living with the White majority in USA, is also considered as a form of protest literature. A piece of art or literature, claiming the additional rights and favors for any group of society, cannot be claimed as the protest form of expression, because it does not fulfill the prescribed criteria. It is therefore, one school of thought does not consider the writings of the African Americans as the true form of protest literature. Larry Neal, America n writer and editor, does not believe such substance as conforming to the criteria of protest literature in a comprehensive way and in its true spirit as well. Neals definition in the Notron Anthology states that Black Arts Aesthetic in not equal to protest literature because protest literature appeals to the white culture elite. As such, it envisions an art that speaks directly to the needs and aspirations of Black America. Protest literature cannot be judged on the basis or disliking of one single community. On the contrary.