Trigonometry/Concepts
From Wikibooks, the open-content textbooks collection
[edit] Usage and Relevance of trigonometry
In trigonometry, there are some concepts which must be grasped by the reader in order to understand the usage and poignance of trigonometry. It has often been asked about why trigonometry exists, and why it is not simply under the umbrella of geometry -- while it is true that trigonometry is a tenet of geometry, its importance gives it the title of trigonometry because it is simply more than just "what is a triangle's length?" and "what kinds of triangles are there?", and should thus be acknowledged.
Similarly, such thought is somewhat superfluous, semantic and away from the principles of mathematics; thinking why a dog is not called "a-furry-thing-sometimes-but-sometimes-not-furry-and-sometimes-barks-when-angry" is the same lines of "Why isn't trigonometry called geometry of triangles?"; if for nothing else, the name is used for referring to something with accuracy and meaning and not for determining what it is a part of. If it were for people to go to the base of every definition every tenet of science, it would end up to some kind of ambiguous mess seen before in explaining our doggy friend.
If you are concerned about the history of trigonometry, which, by all means has importance, then understanding the principles and finer points of its beauty will help you come to the conclusions its contributors came to, hundreds and even thousands of years ago.
[edit] Further concepts and understanding
In order for you to understand trigonometry, this book will provide the necessary foundation in mathematics to help you continue on with complete understanding of the topic, rather than urge you to read another book, and switch back and forth between the two. However, it is beneficial to have an understanding of algebra and basic mathematics to be able to begin the topic of trigonometry with a "running start." Because trigonometry describes entities and their relation to each other, it is naturally expressed through geometry because there are entities which produce ratios, constants and equivalents to each other. These are not expressly difficult to understand, but require some thought when being applied to situations of trigonometry.
The prerequisites of trigonometry are learn similar to those of the principles and prerequisites for any other form of mathematics and are used throughout the explanations in this book. When learning any topic, the fundamentals are re-used repeatedly as a means of achieving higher platforms of learning once other concepts have been understood and analyzed properly. Although this sounds exceedingly difficult to someone who has no idea of analysis and understanding, the use of the terms is merely as a means of describing the tasks which you have to do, or in what way it is best to go about them, and is by no means out of the reach of anyone.
So, for the foundations of trigonometry, the fundamentals are that the student be ready and willing to understand the relation of objects to each-other and their uses between and within other shapes. Of course, because these entities are in relation, they resemble a whole unit which, when broken down must be related with the use of algebra. However, such algebra only involves very basic equations, ratios and fractions and these will be broken down initially to show their logic, but also to reveal paths to the reader which they may not have known, or thought of before.
Of course, with everything that has requirements within other fields, reading other disciplines also helps enhance the ease and accuracy of the skills when they are applied to trigonometry. However, a good axiom for all learning that should be applied here is that you must allow yourself to move to the topics and the discipline itself; do not feel that you are implicitly required to, or that you must learn the concepts, but get to a stage where you, yourself are interested in the topic and feel that reading the topic directly gives you extra depth on the topic.
