Law of Sines and Cosines Essay Example

Law of Sines and Cosines Paper Law of sines In  trigonometry, the  law of sines  (also known as the  sine law,  sine formula, or  sine rule) is anequation  relating the  lengths  of the sides of an arbitrary  triangle  to the  sines  of its angles. According to the law, where  a,  b, and  c  are the lengths of the sides of a triangle, and  A,  B, and  C  are the opposite angles (see the figure to the right). Sometimes the law is stated using the  reciprocal  of this equation: The law of sines can be used to compute the remaining sides of a triangle when two angles and a side are known—a technique known as  triangulation. It can also be used when two sides and one of the non-enclosed angles are known. In some such cases, the formula gives two possible values for the enclosed angle, leading to an  ambiguous case. The law of sines is one of two trigonometric equations commonly applied to find lengths and angles in a general triangle, the other being the  law of cosines. Law of cosines In  trigonometry, the  law of cosines  (also known as the  cosine formula  or  cosine rule) is a statement about a general  triangle  that relates the lengths of its sides to the  cosine  of one of itsangles. We will write a custom essay sample on Law of Sines and Cosines specifically for you for only $16.38 $13.9/page Order now We will write a custom essay sample on Law of Sines and Cosines specifically for you FOR ONLY $16.38 $13.9/page Hire Writer We will write a custom essay sample on Law of Sines and Cosines specifically for you FOR ONLY $16.38 $13.9/page Hire Writer Using notation as in Fig. 1, the law of cosines states that where ? denotes the angle contained between sides of lengths  a  and  b  and opposite the side of lengthc. The law of cosines generalizes the  Pythagorean theorem, which holds only for  right triangles: if the angle  ? s a right angle (of measure 90 °Ã‚  or ? /2 radians), then cos(? ) = 0, and thus the law of cosines reduces to The law of cosines is useful for computing the third side of a triangle when two sides and their enclosed angle are known, and in computing the angles of a triangle if all three sides are known. By changing which legs of the triangle play the roles of  a,  b, and  c  in the original formula, one discovers that the following two formulas also state the law of cosines:

English Narrative Essay Topics

English Narrative Essay TopicsYou may think that English narrative essay topics are going to be boring and dry, but you are wrong. As long as you know what you want to say and when you want to say it, you can write a very interesting essay. There are many possible topics for your story and you will just have to pick one. Here are some English narrative essay topics you can use:Gone are the days when you can only talk about very important figures in history. Nowadays, people are looking for news or their favorite celebrities to complain about how the world is going downhill. Don't be surprised if the next celebrity wants to talk about the weather. A theme like this could turn out to be very interesting. Try it out and see how well you have written on the topic.A lot of English writers find that a focus on something they love the most is very effective. Try to write about what you love to do, so that it might make it in your essay. Some people may not be aware of what kind of subject t hey are really in love with. If you know, just try to talk about it in your narrative essay. There is no need to be ashamed to write about what you love to do, because it might help you write more convincing essay.Another subject, you can discuss is the period in which a certain period of history has come to an end. You might talk about how things came to an end, how different were the end of times, who were the rulers, what happened to some famous people, etc. These are all questions that can be answered by researching. While you may not have access to a library, you can always look online for answers, just to avoid spending too much time trying to look for it yourself.The people of different countries have stories about very interesting stories. You might talk about an interesting example from history, or about a movie that made a lot of people happy. Talk about your own country or about the country where you come from. In this way, you can convince more people to read your articl e. Just make sure that they will get good information.Reading is one of the most enjoyable activities, but many people never take the chance to read a book. Just because they do not know that there is a book that would interest them, it does not mean that they cannot read at all. You can write about any book that you read and make sure that you try to talk about it in your narrative essay.Take some time to check out a website that focuses on local events. You can take advantage of this by putting a story about the occasion in your article. Try to tell it in a way that would make it interesting. If you do not have anything interesting to talk about, just use your imagination and you will be surprised with what you will be able to come up with.So, now you know a few English narrative essay topics you can use. Just have fun while writing and be creative, because there is nothing that can be as fun as an interesting essay.