Carl Rogers’ Theory Of Personality. Personality Theories

Carl Rogers’ Theory of Personality Personality theories suggest explanations for behaviors and how to change them. Multiple personality theories exist however one of the most interesting is the theory of personality by Carl Rogers. Rogers writes, â€Å"the core of man’s nature is essentially positive† (1961, p.73). â€Å"Carl Ransom Rogers (January 8,1902- February 4, 1987) was an influential American psychologist who, along with Abraham Maslow founded the humanistic approach to psychology† (â€Å"Carl,† 2017, para. 1). Carl Rogers was an instrumental humanistic psychologist who received many awards including the first APA award for Distinguished Contributions to Applied Psychology in 1972 (â€Å"Carl,† 2017). Carl Rogers’ made many contributions to therapy†¦show more content†¦McLeod (2014) explains that self-concept has three parts which are self-esteem, self-image, and ideal self. He says Rogers believed self-esteem developed from how our parents interacted with us (McLeod, 2014). Simply, â€Å"self-image is how we see ourselves† (McLeod, 2014). McLeod (2014) mentions that â€Å"Self-image influences how a person thinks, feels and behaves in the world. According to McLeod (2014), our ideal self is who we desire to be. Basically, the closer a persons’ self-image and ideal self are to each other the higher one’s self esteem becomes. Rogers developed Person-centered therapy. â€Å"Rogers’ basic tenet was that if unconditional positive regard (Respect), genuineness and honesty (Congruence), and empathic understanding (Empathy) were present in a relationship, growth and psychological healing would occur† (â€Å"Carl,† 2017). McLeod(2014) suggest that incongruence exist when a person’s self-concept does not match reality. For example, a student who makes good grades on test might think they are a great student, when in reality they never come to class and lie to the teacher with excuses. Accordin g to McLeod(2014) Conditional positive regard is when the person is loved depending on correct and acceptable behaviors (McLeod, 2014). Lastly, unconditional positive regard is where the person is loved and supported no matter what the person does (McLeod, 2014). Orlov Coleman (1992) state, â€Å"to achieve the conditions forShow MoreRelatedCarl Rogers Theory of Personality2519 Words   |  10 PagesCarl Rogers Introduction Carl Rogers is among the small group of enlightened, visionary individuals that stand as giants in the field of psychology. Due to the theories that Rogers developed not only in psychology but in theories of education, he is considered, as Constance Holden writes, †¦one of the grand old men of American psychology and a leading figure in the postwar development of humanistic psychology (Holden, 1997, p. 31). This paper reviews his theory of personality, his approach toRead MoreThe Theory Of Personality : Carl Rogers846 Words   |  4 PagesPsychology Assessment Carl Rogers was a humanistic psychologist who developed the theory of personality. This theory helps us to understand human behaviour by looking at a person’s self-image and their actions and therefore shows that everyone is different. Rogers believed that people can achieve self-actualization through unconditional positive regard, congruence and genuineness. (McLeod, 2014) Self-actualization is when a person can reach their full potential and this happens when their self-imageRead MorePersonality Theory Bandura Carl Rogers3322 Words   |  14 PagesRunning head: Albert Bandura Carl Rogers Compare and Contrast Social Cognitive and Humanistic Theories of Personality to the case study entitled Myesha Course: PSCY3017 Personality Theory II Personality is an intriguing component in psychology vital for the perception of human beings. Understanding and defining personality has proven to be a difficult task. It is so complex, in fact, that no single theory can adequately define it. If one was to ask an ordinaryRead MoreCarl Rogers and His Theory of Personality Essays3414 Words   |  14 PagesCarl Rogers (1902-1987) was ‘the most influential psychologist in American history’ (Kirshenbaum, 1989:11). Since the study of personality began, personality theorists have offered a wide assortment of explanations about behaviour and about what constructs a person. Carl Rogers was the main originator of the ‘person centred’ approach, also referred to as the ‘nondirective’ or ‘client centred’ approach. This essay will offer a brief description about some of the main concepts in Carl Rogers’ personRead MorePersonality Theory: Victor Frankl vs Carl Rogers Essay2368 Wor ds   |  10 PagesPERSONALITY THEORY Ââ€" CARL ROGERS AND VICTOR FRANKL Why is it that man lives up to a certain point not knowing what the meaning of life is. Not knowing what path to follow, not knowing if the energy and courage to discover the truths of ones own existence in this world exist. Some persons will drive past a street child on Cape Town roads and look sideways in horror, quickly lock a car door with an unapparent elbow; warm, safe, and comfortable in the interior of a brand new sports model car. OthersRead MorePsychodynamic And Humanistic Theories Of Psychology1634 Words   |  7 PagesPsychodynamic and Humanistic Personality Theories The study of the human mind is an interesting topic to discuss about, we have many theorists that have come up with many different ideas or theories, in how to evaluate the mind of humans, two main ways to study the mind in psychology are psychodynamic approach and humanistic approach. Even though these theories are to evaluate human minds they have different views in how the mind works. In psychodynamic approach, the way the mind is viewed is thatRead MoreComparison of Theories on Personality Essay examples1273 Words   |  6 PagesComparison of Theories on Personality Abstract This paper is a comparison of three different viewpoints on the subject of personality. Carl Jung, B.F. Skinner, and Carl Rogers all had very different outlooks on what defined someone’s personality. As an added feature I have included myself as a theorist because my views are also different from the previous mentioned theorists. This paper will also look briefly into the background of each theorist because their views on life began in theirRead MoreSigmund Freud And Humanistic Theories Of Psychology1636 Words   |  7 PagesIntroduction The reading of personality has a thick layer of theories in psychology and is one of the most important fragments of psychological history to this day. This paper will compare and contrast the differences between the great theories of the psychodynamic theory from Sigmund Freud and the humanistic theory from Carl Rogers. These two theorists have different views of how personality is developed, with both theorists influencing the world of psychological personality to this day. Disputes betweenRead MoreFreuds and Rogers Theories of Personality Psychotherapy1004 Words   |  4 PagesFreuds and Rogers Theories Personality Psychotherapy A comparison of Freud and Rogers theories of personality and psychotherapy Personality is the description of an individual through how the individual demonstrates his or her emotions and building relationship and their behavioral patterns. Two neurologists developed two theories to explain the formation of personalities. They were neurologist Sigmund Freud and psychologist Carl Rogers. Rogers and Freud worked in the field of psychotherapyRead MoreThe Theories Of Personality Theories1124 Words   |  5 Pagesimportant theories regarding personality. Some of these theories are still relevant to our world today. These theories have helped form humans and they have also changed the way we think and the way we do things. There are many different forms of personality theories that have shaped the world for us: Biological, Behavioral, Psychodynamic, Humanist, Trait, etc. Biological theories are based on genetics and they believe that genetics are responsible for personality. Behavioral theories suggest that

Evaluate the Organization’s Involvement and Responsibility to the Community free essay sample

Evelyn Hamilton, Aaron Pobleh and Regina Taylor CJA/474: Managing Criminal Justice Personnel November 26, 2012 Instructor: Pam McIver The term motivation and empowerment is a universal concept that is hoped to work towards the good of any organization. Motivation and empowerment does not come from rewards to employees but instead, recognition, responsibility and advancement. Leaders who are effective in motivating and empowering their staff have acquired a great achievement, which can increase efficiency, and self development of skills and abilities. When employers are concerned about the welfare and needs of their staff, this provides trust among staff. The purpose of this paper is to compare motivation and empowerment, define the components of empowerment, analyze the implications of empowerment and delegation in a criminal justice organization and analyze the role of trust in personnel issues. Compare motivation and empowerment Motivation and empowerment are two words that are very popular in every workplace. Generally when one mention motivation, everyone would think it is what employer gives their employees, unfortunately, motivation in the workplace goes way far beyond that. Motivating your employees gives them authority to do more work for you and do it better. According to businessdictionary. com, motivation is both internal and external factors which desire and energize people to become committed to a job, role, or subject, or to strive to reach a goal. While empowerment is management practices which allow the sharing of information, power, and rewards with employees so that they can take initiative, and make decision to solve problems, and improve themselves as well as enhance their performance (www. usinessdictionary. com). Everyone need to feel empowered regarding their work ethic on the job or being assertive in life challenges and changes, but without the key elements of self-motivation, assertiveness and the ability to make good decision how would they be able to motivate others. Mangers of an organization should show through their behavior and actions how provide the necessary skills to be productive and efficient. This in turn will produce hap pier employees. Define the components of empowerment In order to be an effective leader a person would need to be empowering by those below them and therefore allow them to take initiative on their own. A leader that has poor management skill fails to empower anyone underneath him. For example, an office manager as well as a beginner officer within the work place or in the field must feel good about performing on their own and not feeling they will be overly scrutinized regarding their errors. They must not fear the aftermaths or punishments for taking individual decision making. When this happens, employees began to shun management for fear always doing something wrong. Employers should provide positive communication to their staff (National Empowerment Center). There was a research designed to examine the concept word of empowerment in this programs sponsored by multiple examiner of the criminal justice it was first anticipated to create a working definition. After research the â€Å"elements of empowerment were identified, including access to information, ability to make choices, assertiveness, and self-esteem. Empowerment has both an individual and a group dimension (Tom Roger, 2011). This research studied participants in self-help programs for people with no self-motivation and the need for encouragement. At the beginning of the study,† it was stated numerous of the individuals involved empower in their research. It’s obviously the important theory concerning the essential to defining meaning of empowerment as part of the development. Although it â€Å"recognized that empowerment had elements in common with such concepts as self-esteem and self-efficacy, these concepts did not fully capture what was considered a distinctiveness about empowerment† (Tom Roger, 2011). In an earlier â€Å"debates empowerment was† considered â€Å"complex, multidimensional concept, and that it described a process rather than an event†. It was never â€Å"believe that an individual had to display every quality on the list in order to be considered† empowered (Tom Roger, 2011). Analyze the implications of empowerment and delegation in a criminal justice organization Today the style and practices of police leadership is changing rapidly. The term shared leadership is one being used by many police chiefs all across the country. They believe that this approach to management by sharing power and influence to individuals within the organization, who are otherwise hierarchical unequal, will view their leadership as a leadership which looks at the broader aspect of giving authority to employees which will allow them to make decisions, solve problems, and be held accountable for their actions (Mussellwhite, 2007). Whenever officers are empowered they become dedicated to their jobs. Because they are given the skills, resources, authority, opportunity to be motivated and committed to their jobs, roles, or duties. Something which is refers to as being dedicated. Employees empowerment in a police department which delegate assignments, allow officers to take responsibility of their jobs results. It also allows them to make decisions about it. When officers are delegated with responsibilities, it makes them think in decision making, take control, behave, and take actions responsively, because they know that they will be held accountable for their actions. Police departments that apply employee empowerment create an environment in which their officers are empowered, productive and are happy in their jobs. Such police departments do not limit their employees to information (Heathfield, 2012). Analyze the role of trust in personnel issues. The role of trust in personnel issues involves how employees relate and respond to their employer. For example, if an employer is more concerned about getting the job done employees will pick up on that and will respond to their employer in a negative way. But when employers’ show that they truly care about their employee’s well being they will respond in a positive way. It would be in the organizations best interest for employers to take time to get to know their employees. Employers should empower their staff by allowing them to make important decisions in reference to their day to day duties. This will cause employees to respect their employers which will also lead to trust. When employees trust and respect the organization they will do the best possible work they are capable of doing. This in turn will lead to accountability on the part of the employee (Mussellwhite, 2007). When an employer gains the trust of their staff, they will know how to motivate each individual person for the best outcome of the organization. Employees understand that no organization is a perfect organization. When employees know and feel important to the organization, respect and trust will deepen. Respect and trust will take an organization to higher creativity and increased efficiency (Forbes. com, 2009). Positive communication is the cornerstone to empowerment and trust within an organization. When employers take the time to consider their staff opinions and feedback on daily operations, this can cause higher productivity and increase efficiently. Employers should share information about the organization with their staff. This provides for a clear picture of how the organization is progressing or not progressing. This also produces trust among employees because employers trust their staff (Mussellwhite, 2007). Conclusion In conclusion, this paper compared motivation and empowerment, defined the components of empowerment, analyzed the implications of empowerment and delegation in a criminal justice organization and analyzed the role of trust in personnel issues. Motivation and empowerment is about providing production and management guidelines to employees and then allows them to operate in an independent manner. Empowerment and delegation within the criminal justice system involves sharing power and influence to individuals within the organization, who are otherwise hierarchical unequal. This leadership looks at the broader aspect of giving authority to employees which will allow them to make decisions, solve problems, and be held accountable for their actions. The components of empowerment are about communication, feedback and productivity. Employees should be trained properly so that trust is gained through empowerment. A motivated and empowered employee will respect and trust the organization which will lead to accountability and responsibility. Leaders can gain great achievement when they effectively motivate and empower their staff into self development of skills and abilities. References Chris Musselwhite, 2007. Inc. Motivation=Empowerment; retrieved on November 22, 2012 from www. inc. com/resources/leadership/articles/20070801 Employees Empowerment: How to Empower employees. Retrieved on November 22, 2012 from www. humanresources. about. com/od/employeeempowerment Empowerment in the Workplace ttp://ezinearticles. com/? Empowerment-in-the-Workplaceamp;id=6541445 Make sure your employees trust you or else. Forbes. com 2009. Retrieved from http://www. forbes. com/2009/03/23/trust-respect-employees-leadership-managing-blanchard. html. National Empowerment Center Article www. power2u. org/articles/empowerment/workingdef. html Susan Heathfield. 2012. What is Empowerment; Retrieved on November 22, 201 2 from www. businessdictionary. com/definition/empowerment. html What is Motivation; Retrieved on November 22, 2012 from www. Businessdictionary. com/definition/motivation. html

Yusef Komunyakaa Poems And Their Themes Essay free essay sample

, Research Paper The common subject in Yusef Komunyakaa? s verse form is the Vietnam War. He focuses more on the experience of it, instead than the grounds for the war itself. In some of the verse forms, the issue of race was more apparent than others. The race of all work forces was embraced in? Camouflaging the Chimera? . The first word of the verse form foreshadows the insignificance of colour and the value of brotherhood. ? Camouflaging the Chimera? shows the double, frequently diametrically opposed images. Acknowledging that the horrific, absurd, and helter-skelter frequently lurk behind delusory frontages, the writer vividly describes the soldier? s attempts to intermix in with the natural environment, ? We tied subdivisions to our helmets/ We painted our faces A ; rifles/ with clay from a riverside? All of the military personnels were the same colour so. The soldiers used the same thing to camouflage their tegument that would be used to cover their caskets and finally be their concluding fini sh. We will write a custom essay sample on Yusef Komunyakaa Poems And Their Themes Essay or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page This is one destiny they all have in common regardless of the race. The verse form entitled? Hanoi Hannah? embraces the race of inkinesss. It is a free-spirited, inspirational verse form with some purpose to be a reminder of some of the good things back place, ? Hello, Soul Brothers. Yeah/ Georgia? s besides on my mind. ? Even for those African americans who did non populate in Georgia idea of the province as a? black adult male? s topographic point to populate? . There was ever excitement in Georgia. Komunyakaa besides acknowledges the torment of female parents, married womans, and lovers left buttocks. He doesn? t discriminate with colour. He brings to life images of? adult females left in doorways/ making in from America. ? In the verse form? Confronting It? , all Vietnam veterans are embraced. The gap line rapidly dismantles any? colour? association with the beloved Vietnam Veteran Memorial. ? My black face slices, / concealing inside the black granite. ? Color is no longer of i mport when you have all fought the same battle, shed the same blood, and been shot with the same slug. All of those who are subsisters of the war are? confronting? the memories of it all ; ? I see the dumbbell trap? s white flash. ? Many soldiers were killed by dumbbell traps instead than combat heavy weapon. In? Confronting It? there is a conflict between world and do believe, ? Names shimmer on a adult female? s blouse/ but when she walks away/ the names stay on the wall. ? It is a beautiful commemoration for the vets, but a really dejecting one besides. The names can non be removed by anything, including the head. Those who gave their lives for the state ( black and white ) all portion the same end–the black wall and the black grave. The embrace of race is noted in? Hanoi Hannah? , but so is the transcending of race. The verse form is about the confusing head of a black adult male in the Vietnam War, ? Soul, Brothers, what you deceasing for? ? And at this clip, oppugning the ground for being loyal to a state that hates you was on most African- Americans? head. What were they contending for? As soldiers of African decent made their manner back into the community after functioning dependably and uprightly in the military, many were denied employment, lodging, preparation, and veterans benefits. It was besides obvious that many Americans thought that the whole thing with Vietnam was pathetic. Peoples viewed the Whites as stalwart, but the inkinesss were considered brainsick. The rubric of Komunyakaa? s 2nd aggregation on the Vietnam War, Dien Cai Dau, which means? loony? in Vietnamese, displays the resistance for a black adult male in the war. All of America was roasting them for their attempts while praising the re mainder, ? You? re icky shootings, GIs. ? Regardless of a adult male? s cultural background, if he fights for his state, his state owes him service, glorification, and above all else # 8211 ; gratitude. Bibliography Komunyakka, Yusef # 8220 ; Hanoi Hannah # 8221 ; Fitzgerald Publishing 1985.

the black plague essays

the black plague essays The Black Plague was a great European disaster that had many affects of the people living at that time. Though there may be controversy today over its precise significance, no one would to-day deny that the black plague was of the greatest economic and social importance as well as hideously dramatic in its progress. (form the book The Black Death by Phillip Ziegler) In the early 1330s the black plague started to form and the first place it struck was in China. The bubonic plague was basically fleas on rodents such as rats but, fleas can also transmit the disease to people as well as rats but mainly rats that the fleas transmitted this horrible plague into. The spread of the plague started in China very fast since that it was the most over populated country the plague naturally spread very quickly. Since China was the one of the busiest of the worlds trading nations, it was only a matter of time before the plague was spread into western Asia and Europe. In October of 1347, several Italian merchant ships returned from a trip to the Black Sea, one of the key links of trading was with China. Inside the ship there was already people suffering from the deadly virus. Soon when the ship arrives at there location, which is Sicily in Italy. Only within a number of days the disease spread to city and to the countryside. An eyewitness tells what happened and this is what he said: Realizing what a deadly disaster had come to them, the people quickly drove the Italians from their city. But the disease remained, and soon death was everywhere. fathers abandoned their sick sons. Lawyers refused to come and make out wills for the dying. Friars and nuns were left to care for the sick, and monasteries and convents were soon deserted, as they were stricken, too. Bodies were left in empty houses, and ...

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.

Sleepy Inn Motel Case Study Example | Topics and Well Written Essays - 1000 words

Sleepy Inn Motel - Case Study Example Even though it is near a quickly expanding resort region, this represents long-term growth and Huang needs to change his revenue stream much more quickly. Huang faces competition from Hilton Inn, Ramada Inn, and Best Western as well as many other lower-priced hotels similar to his own. His larger competition represents very well-known brands with a great deal of brand recognition and brand loyalty by a variety of mixed demographics. Further, since the only promotional material for this region are two billboards operated by the Tourist Bureau, Huang simply cannot rely on the marketing competency of this agency to fill his capacity rates. Huang maintains a low-cost pricing policy that he had established in the hopes that it would bring enough attention to make travelers choose Sleepy Inn Motel over other well-established branded competition. However, the problem here is that 68 percent of visitors to the region are younger couples and older couples with no children, two demographic gro ups that typically have much more access to higher financial resources. This is likely the reason why Huang witnesses visitors turn into his parking lot, but never enter the building. Once a hotel has established brand recognition and brand loyalty, it is difficult for a smaller, virtually unknown name to compete effectively without very intensive integrated marketing campaigns that must be managed and updated constantly. Further, the study conducted of local tourist needs identified that 78 percent believed it important to have recreational facilities before choosing to make a purchase. This is a substantial volume of customers and it is likely that Huang’s lack of a swimming pool is the reason why individuals turn in, but then leave in favor of the larger hotel brands. The costs of adding a swimming pool and other recreational facilities, such as a gym or child’s area, would be a budgetary problem for Huang who is currently experiencing lower-than-average occupancy r atios. Days Inn does not require extensive financial investment and this is a very well-known brand with many different loyal demographics, including military, school teams, business travelers, and senior citizens. Days Inn already has their own well-established marketing campaigns that include on-air promotions such as the described promotion with Blue Bonnet margarine and also a senior citizen discount card to invite incentive purchases. Since Days Inn also has a dedicated customer reservation line, a travel magazine, and a website, this represents the best long-term option for Huang under a franchising agreement. Days Inn might also allow Huang to establish his own unique in-house marketing literature if this were required which could be determined at the time of contract negotiation. The amount of money demanded under the franchising agreement, by Days Inn, is only eight percent of total room revenues. To support choosing Days Inn rather than operating his own brand, a brief rev enue analysis is required. At $45 per night, with only 55 percent of occupancy, this represents $10,395 weekly in gross revenues. By moving under the Days Inn brand, at $70 per night and 68 percent of occupancy, Huang will earn $20,090 in gross revenues weekly or $80,360 monthly. This is almost double what Huang is

Global warming Research Paper Example | Topics and Well Written Essays - 2000 words - 1

Global warming - Research Paper Example The high increase in temperatures has resulted in global warming, which has negatively affected the environment. Goldstein (2009) reports that the earth’s surface has experienced about 0.8% rise in temperature since 20th century. A report by the Intergovernmental Panel on Climate Change (IPCC) in 2007 projected that the earth’s surface temperatures could increase from 1.1 to 2.9 oC in the 21st century (Goldstein, 2009). The increase is also expected to continue unless something is done to stop activities perceived to cause global warming. A report by the BBC also indicated that the world would be six and a half degrees warmer than it is today by the time a child born today reaches 80 years. Global warming has mainly been blamed on human activities taking place all over the world. However, many researchers have demonstrated that global warming is the result of greenhouse emissions into the environment. In this regard, scientists have shown that global warming occurs due to carbon emissions released into the environment, which blocks the ozone layer thereby preventing the sun’s light and heat from reaching the earth’s surface, notes Goldstein (2009). ... Research indicates that many countries in the world currently depend on fossil fuels as the main energy source. In fact, Victor (2011) reveals that more than 90% of energy all over the world currently comes from fossil fuel. According to Victor, the negative impacts of global warming are already being felt on the earth today. The impacts include persistent bush fires, glacial movements, perennial drought, flooding, typhoons and rising sea levels just to name but a few. However, since global warming is the direct result of human activities, it is viewed in an ethical angle. It is unethical for human beings to engage in activities that promote global warming. This is based on the fact that the consequences of global warming stretches beyond the good purposes for which the activities are meant. This paper will explain why I consider activities promoting global warming as being unethical. Global warming is indeed causing havoc in the world over. Its impacts are adversely affecting all na ture-human beings, oceans, forests, farms, mountains, and coasts among others. According to Fern (2003), the global warming caused by greenhouse emissions is a direct result of human activities such as burning of charcoals, industrialization, farming, the use of fossil fuel and other activities that release carbon into the atmosphere. Ethically, the most fundamental question we are often confronted with concerning particular environmental ethics pertains to the obligations we have regarded the natural environment (Keller, 2010). In this regard, if the conviction regarding the obligation is that we as human beings will suffer as a result of the failure to act appropriately, then this is regarded â€Å"anthropocentric,† which