If you have got an assignment that requires dealing with trig derivatives, finding the derivative of a trigonometric function or other manipulations with triangles, you are most probably will have to deal with the differentiation of trigonometric functions. This is a mathematical process that deals with all the above-mentioned problems. As a matter of fact, when it comes to trig derivatives, the majority of students get scared even of the mathematic term, if not to mention the very process of trigonometric functions processing, etc. Indeed, this is one of the most difficult and complicated aspects of mathematics that students have to deal with during their studies. It requires spending a lot of time, significant efforts and lots of practice to get essential skills for solving such mathematical problems. On the other hand, practicing trigonometry, as well as other branches of mathematics (particularly, geometry), helps develop and improve a number of important skills, such as logical thinking, analyzing, etc. In this article, you will learn to cope with the above-mentioned problems, and learn some essentials of mathematics, especially geometry and trigonometry.
As a rule, the most common trigonometric functions consist of sin(x), cos(x) and tan(x). Derivatives can be used for different purposes. For example, they are helpful when obtaining useful characteristics concerning graphs (here, we are talking of maximum, minimum, slopes, peaks and so on). Also, you can apply trig derivatives to the complicated equations of the graph without even turning to the help of the graphing calculator. However, obtaining the derivative can never be easy, as long as you need to have some basic knowledge and elementary practice in this regard, as well as be aware of different tricks. Look what essential steps you need to undertake in order to deal with derivatives:
These guidelines are useful when looking for the trig derivatives, although they don't cover all the details that you may face during the process of differentiation. In order to increase your chances to succeed in this uneasy deal, keep reading further and you will find some useful tips in regard to this issue.
There are common tricks that some students use in order to make their studying of trigonometry, geometry or other branch of mathematics much easier. As for the trigonometry, we suggest you following tips that are provided below:
Having said that, not only the knowledge of the trigonometric functions, the methodology how to use them and awareness of their properties is important to succeed within studying trigonometry, but also you need to have some theoretical background. To get some of theoretical knowledge in the area of trigonometry, keep reading further.
Trigonometry is one of the branches of mathematics that deals with studying of properties, specificities and characteristics of triangles, such as the relationships including lengths and angles of different triangles. The term «trigonometry» has originated from the Greek language and can be translated as the «measure». The history of this branch of mathematics has started more than two thousand years ago and originated from the astronomical studies and basic geometry.
When trigonometry appeared on the list of other sciences, it affected the world of science a lot. The astronomers of that time noticed that there were relationships between the sides of a right-angle triangle and the angles of the geometry figure. That relationships are expressed in such a way, that if you know at least the length of only one side of a right-angle triangle, together with the value of at least one angle of the triangle, you can find out the two other angles by means of determining them algorithmically. All these calculations were called later as trigonometric functions and they were exactly the functions that are used even today. They are successfully applied in pure and applied mathematics. Apart from this, trigonometric functions are widely used when dealing with wave equation, they can be applied to comprehend the cyclical phenomena, as well as to the electrical and mechanical engineering, astronomy, biology, acoustics and music and even ecology. In addition, trigonometry is considered to be the foundation of land surveying (it is the technique/science/profession that deals with identifying three-dimensional position of points and determining the angles, as well as distances between them).
Usually trigonometry is associated with triangles, which is right, but only if you mean planar right-angle triangles. Even though trigonometry can still be applied to the non-right-angle triangles, this is a quite rare occurrence, because in most of cases it is much more convenient to divide the non-right-angle triangle into two other triangles that would be the right-angle ones. Thus, you will have to deal with only right-angle triangle anyway. Trigonometry essentials are taught at middle schools, high schools and sometimes in colleges.
Sumerian scientists are widely known due to numerous discoveries that that have made and due to significant achievements and contributions to the world of science of that time, which resulted in further exploration and research of the world. Among the studies that Sumerian developed, there was trigonometry, as long as they studied a lot the properties of the ratios of the sides of the equal triangles. Their studies, however, didn't appear to be an organized and systematic method for solving important trigonometric problems, such as measuring angles and sides of triangles.
Apart from Sumerian, Greek mathematicians also made a number of significant contributions to the studies of trigonometry. Such outstanding scientists as Euclid and Archimedes dedicated a lot of their works to the study of chords and their properties, as well as to the circles and inscribed angles in them. In addition, they managed to prove the theorems from which the trigonometric functions that we know and use today originated. It has to be mentioned, however, that their methodology and strategy of presenting these theorems were rather algebraic than geometric.
Generally speaking, trigonometry as we know it today originated in Surya Siddhanta. The properties of modern sine convention were documented for the first time in the fifth century by an outstanding Indian scientist in the field of mathematics and astronomer known as Aryabhata. Later, these works were translated into different languages and the knowledge of trigonometry widespreaded all over the world. Soon, Islamic scientists, particularly mathematicians were applying all the six trigonometric functions, exploring their properties and tabulating their values, as well as using trigonometrical functions in terms of spherical geometry.
Numerous discoveries in the area of trigonometry, and the knowledge of trigonometric functions and their applications reached the countries of Western Europe in the sixteenth and seventeenth centuries, although at that time, mathematicians used only the basic concepts concerning trigonometry without going deeper in that issue.
There is a great number of applications of trigonometry, as well as of trigonometric functions. Different techniques are applied in the area of various sciences and even to the everyday life. For example, triangulation as one of trigonometry techniques is widely used in astronomy with the purpose of determining distances between the stars and between the Earth and other objects in the space. The technique of triangulation is also used in geography with the purpose of determining distances between different countries or objects on the planet. Also, it is important to mention that such trigonometric functions as sine and cosine play considerable role in when describing light and sound waves.
Areas that take advantages from the usage of trigonometric functions and trigonometry as a whole, include astronomy (first of all, it helps with locating different positions of objects in the space), navigation (in almost all areas of the Earth, including oceans, aircraft, space and so on), the theory of music, optics, acoustics, seismology, electronics, architecture, all branches of natural sciences, economics, crystallography and development of the computer games, mechanical and electrical engineering, geodesy, etc.
The information provided in the article is helpful when dealing with trigonometry, trigonometric functions and when solving trigonometric problems. If you need additional help, you may use the following services: