Figuring out what is secant and other trigonometric functions
Dealing with geometry has never been easy to anyone, with the exception of those students who have strong mathematical skills and find it interesting to learn. Trigonometric functions, which are sometimes also called as circular functions, are used for dealing with an angle. These functions play a significant role in the studies of mathematics because they serve to create relations between a triangle and its basic characteristics, such as the lengths of its sides. Apart from it, trigonometric functions are necessary when it comes to learning and modeling different periodic phenomena. Students need to be aware of what is secant because this function is one of the basic functions in geometry together with such functions as tangent, sine, cosine and a couple of others. As a matter of fact, trigonometric functions can be used in solving a wide range of mathematical problems, they help find out and calculate unknown lengths in different kinds of triangles and their angles. Also, these functions are widely used in such fields as engineering, navigation and physics.
The question of what is secant can be enlightened in the context of various sciences and branches of sciences. For example, if to discuss secant in the context of geometry, we should mean a certain line that serves to intersect two points on a particular curve. The word «secant» was originated from the Latin language a very long time ago and was used in the meaning of «cut».
If to discuss trigonometric functions, including secant in the context of algebraic geometry, which is a separate branch of mathematics, we should mean secant variety that is usually used when dealing with studying zeros of multivariate polynomials. Apart from the above-mentioned fields of usage of secant, it is mostly used in trigonometry and represents one of trigonometric functions. When calculating secant, you should use special formula, where in order to define it you will have to deal with the ratio of the length of the hypotenuse of a triangle and the lengths of the adjacent side, appropriately.
Having said that, you most likely will have to deal with secant when studying trigonometry. As a rule, students find this discipline one of the most difficult, it takes a lot of time and efforts to deal with it. Taking this into consideration, we provided some tips and guidelines that may help you study trigonometry, learning what is secant and how to apply it when solving mathematical problems. Therefore, keep reading carefully.
Historical overview of the origins of trigonometry
Mathematics is a very broad science that has a lot of branches, categories, concepts and deals with a wide range of problems. One of its branches is trigonometry, which can be learned in high schools, colleges and universities, depending on the specialization. Trigonometry deals with studying such geometric figures as triangles. Trigonometry basics are usually taught in middle schools and high schools, but in a more grounded manner this discipline can be also taught at higher levels of education. Generally speaking, trigonometry can be associated with geometry figures and in most of cases related to right-angle triangles, the basic property and characteristic of which is that such kind of triangles has one angle that is equal to ninety degrees.
As for the history of the geometry as a science, it has started in ancient times, when people were doing researches concerning angle measurement for building purposes or in the context of astronomy, which is considered to be the first science in the world. Ancient scientists were exploring different kinds of triangles and made a lot of significant discoveries in this field, all of which are actual even today. They studied the ratios of the sides of geometric figures, the properties of all these figures, made up different theorems that are used today in such branches of mathematical science as algebra, geometry, trigonometry and many others.
How to study trigonometry
At first sight, understanding of even basic concepts of trigonometry may seem very difficult and overwhelming. However, if to find the right approach to learning this branch of mathematical science and follow it, while making some efforts, you will see that it can be easy enough. Below, we provided a number of steps that you will have to undertake in order to make success.
- A good starting point could be if you fresh up your elementary mathematical knowledge and skills. By this, we mean the basic knowledge of algebra, geometry and some knowledge in the field of algebraic manipulation. As for the last, it is one of the most essential skills in mathematics, so without practicing it you will not go really far.
- The next step would be to brush up your skills in essential geometry. This branch of mathematics is related to trigonometry most of all and it plays a vital and significant role in dealing with all kinds of trigonometric problems. Therefore, learn all the properties of geometric figures, their characteristics, types and so on.
- To begin with, you will have to learn to deal with right-angled triangles first of all. They are not really difficult to study and this knowledge will allow you to have a good grasp of essential trigonometric skills. Therefore, get familiar with the properties of the sides of the right-angled triangle, learn three ratios of trigonometry and how to calculate them.
- Once you learned something about right-angled triangles, you may proceed to studying non-right triangles. The difficulties in studying this geometry figure appear because it doesn’t have the right angle (which is why it is called that way) and it is not that easy to do necessary calculations with it, as it is with the previous figure.
- The next step would be learning to calculate the angles. To deal with this task, you will have to learn a number of specific formulas, which will allow you to investigate the properties of geometric figures and solve geometric problems.
- Learn trigonometric functions. While undertaking this step, you will have to learn what is secant, as well as other functions such as cosecant and cotangent. Here, you will also have to get familiar with specific formulas that will allow you to calculate and find out essential data when solving geometric problems.
- Once all the previous steps are undertaken, you will have to dedicate certain amount of time to practice. It is a commonly known fact that practice makes perfect. Therefore, the more geometry problems you deal with, the better skills you will have and you will learn all the essential formulas by heart.
- Learn how to solve trigonometric equations. If an equation includes one (or more than one) trigonometric function, it is called a trigonometric equation. There are different ways of solving this kind of equation, including manipulation, dividing the equation by a geometry term and many others.
When undertaking all the above-mentioned steps, keep in mind that mathematics, including all its branches and supporting sciences, is a discipline that requires thinking a lot. Even if you know perfectly all the formulas, it will never give you any guarantee that you will solve a difficult geometry or trigonometry problem. You need to think a lot, think thoroughly and logically and this is the best way to make success in this field of studies. In addition, it is important that you review all the formulas, theories and geometry concepts from time to time in order to make sure that you still remember all the essential information and have proper knowledge.
Having said that, there is a specific trick that helps many students to deal with trigonometry. You should remember that all the existing trigonometric functions have a particular feature, distinguishing them among other functions in mathematics. They are all periodic. It means that all of them tend to repeat their properties and values after every specific angle.
The usage of trigonometric functions
Calculating of trigonometric functions has been researched at times, when the scientists didn’t even know such term as «trigonometry». They used these functions together with the first mathematical tables, which were an integral part of educating students in the earliest universities in the history of the world. At that times, trigonometric functions were very useful not only for studying astronomy, but also for dealing with such matters as creating different buildings.
While today trigonometry is mostly associated with one of the disciplines that students deal with during their studies at different levels of education, this branch of mathematics is very helpful in a wide range of other matters. First of all, it is still applied to exploration of space, especially when it has to be decided where to allocate different celestial objects, etc. This discipline is also applied when dealing with navigation, when it comes to defining locations on the oceans, in the air and space. In addition, we may face trigonometry when dealing with biological science, with medicine, chemistry, economics, arts (especially music theory) and a great variety of other fields of human activity. Therefore, even if you are not going to become a mathematician, it doesn’t mean that you will never have to deal with trigonometry. This discipline is almost universal and trigonometry skills may appear to be helpful in fields that at first sight have nothing to do with mathematics. Apart from all that is said above, this discipline is useful for improving and developing thinking, decision making process, logical thinking and analysis and a number of other skills. Dealing with trigonometric problems and solving them requires much attention, investigation and brainstorming, not only using of particular formulas.
Information provided in this article is useful for those students, who want to learn trigonometry, find out what is secant and other functions and understand the basic principles of this branch of mathematics, as well as get familiar with the origins of this discipline, its history and ways of applying it in real life. If you follow the provided steps carefully, spend some time and make certain efforts, you might be surprised that it is not that difficult as it may seem and more than that, you might even enjoy the process when learning trigonometry. Having said that, we would like to inform you that in case if you find any difficulties with studying trigonometry or any other discipline, as well as if you need assistance with accomplishing different kinds of writing assignments, you are always welcome to use professional help of experienced writers. This is a very helpful and reliable way to get your writing assignments accomplished without spending much time and efforts. Below, we provided some of the services that you may consider to be a good way to meet challenges that the student life throws into you.
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