Trigonometry is a branch of mathematics that studies triangles and periods. Trigonometric functions are used to describe the properties of each angle, the relationships between the various elements of the triangles and the graphs of the periodic functions. Learning trigonometry helps to understand and visualize these relationships, periods and to plot their related graphs. If you combine study at home with constant attention in the classroom, you will be able to learn the basic concepts of this subject and probably notice the applications of periodic functions in the world around you.
Steps
Part 1 of 4: Focus on Major Trigonometric Concepts
Step 1. Define the parts of a triangle
The central core of trigonometry is the study of the relationships present between the elements of a triangle, which is a geometric figure with three sides and three angles. By definition, the sum of the internal angles of a triangle is 180 °. You should familiarize yourself with this figure and the terminology to be able to learn trigonometry. Here are some of the more common terms:
- Hypotenuse: the longest side of a right triangle;
- Obtuse: an angle with an amplitude greater than 90 °;
- Acute: an angle with an amplitude less than 90 °.
Step 2. Learn to draw the unit circle
This allows you to resize any triangle proportionally, so that its hypotenuse is equal to unity. This is an important concept because it relates trig functions, such as sine and cosine, to percentages. Once you understand the unit circle, you can use the trigonometric values of a given angle to troubleshoot the triangles that contain it.
- First example; the sine of an angle of 30 ° is 0, 5; this means that the opposite side at an angle of 30 ° is exactly half of the hypotenuse.
- Second example: This relationship can be used to find the length of the hypotenuse in a triangle with an angle of 30 °, where the side opposite that angle measures 7 cm. The hypotenuse is equal to 14 cm.
Step 3. Learn the trigonometric functions
There are six basic functions for understanding this matter; all together they are able to define the relationships of the elements of a triangle and allow to understand the peculiar characteristics of this geometric figure. Here they are:
- Breast (sin);
- Cosine (cos);
- Tangent (tg);
- Secant (sec);
- Cosecante (csec);
- Cotangente (ctg).
Step 4. Think about relationships
One of the most important things to understand about trigonometry is that the functions described above are all related to each other. Although the values of the functions of sine, cosine, tangent and so on have their specific applications, they are however the most useful because of the relationships that exist between them. The unit circumference is able to resize these relationships, so that they are easily understood; when you can master it, you can use the relationships it describes to demonstrate other problems.
Part 2 of 4: Understanding the Applications of Trigonometry
Step 1. Understand the basic uses of trigonometry in academia
In addition to studying this subject out of simple love of mathematics, scientists and mathematicians apply the concepts to real life. Trigonometry allows you to find the values of angles or linear segments, it can also describe any periodic behavior by graphing it as a trigonometric function.
For example, the movement of a spring bouncing back and forth can be described graphically with a sine wave
Step 2. Think about cyclical happenings in nature
Sometimes, people have a hard time grasping the abstract concepts of mathematics or science; if you realize that these principles are actually present in the real world, you can often see them in a different light. Look at things that occur cyclically and try to relate them to trigonometry.
The moon follows a predictable cycle that lasts about 29 and a half days
Step 3. Visualize how repetitive natural events can be studied
When you realize that the world around you is full of these kinds of phenomena, start thinking about how you could study them in a precise way. Consider the appearance of the graph representing these cycles; starting from it you can formulate a mathematical equation to describe the observed event. This analysis gives trigonometry a practical meaning that helps to better understand its usefulness.
Consider measuring the tide of a particular beach. During the high tide phase, the height reaches the maximum peak and then reaches the minimum one in the hours of low tide. From the lowest level, the water moves towards the beach until it reaches the highest level and this cycle is repeated endlessly; it can therefore be represented in a graph as a trigonometric function, specifically as a cosine wave
Part 3 of 4: Study in Advance
Step 1. Read the chapter
Trigonometric concepts are often difficult to understand on the first try; if you read the textbook chapter before it is dealt with in class, you have greater command of the content. The more times you come into contact with the subject of study and the more connections you are able to make on the various relationships present in trigonometry.
By doing this, you can identify the topics you have the most trouble with before class
Step 2. Keep a notebook
Reading the textbook is better than nothing, but this subject cannot be learned only by studying in depth the various chapters; write detailed notes on the topic you are reading. Remember that trigonometry is a "cumulative" subject, the concepts are developed on each other, so having the notes of the first chapters helps you to better understand the content of the following ones.
Also write down any questions you want to ask the teacher
Step 3. Troubleshoot the book
Some people are able to visualize trigonometric concepts well, but others have a lot of difficulties. To make sure you have internalized the topic, try to solve some problems before the lesson; that way, if you come across unclear passages, you already know what kind of help you will need in class.
Most textbooks provide problem solutions on the back, so you can check the work done
Step 4. Bring study materials to class
Having the notes and practical problems at your disposal, you can have a point of reference; By doing so, you can also review the topics you have learned and remember those for which you need further explanation. Be sure to clarify any concerns you have listed as you read.
Part 4 of 4: Taking Notes During the Lesson
Step 1. Use the same notebook
The concepts of trigonometry are all related. It is best if all the notes are in the same place in order to review the previous ones. Choose a notebook or ring binder that you use only for studying trigonometry.
You can also use the notebook to solve problems
Step 2. Make this subject your priority in class
Avoid using explanation time to socialize or do other subject assignments. When you are in the classroom, your mind should be completely focused on the lesson and practical exercises; write down everything that the teacher writes on the blackboard or of which he emphasizes the importance.
Step 3. Pay attention in class
Volunteer to solve problems on the board or share your own solutions to the exercises; if you don't understand something, ask questions. Keep communication open and fluid as much as the teacher allows; by doing so, you can better learn and appreciate trigonometry.
If the teacher prefers to give a lecture without being interrupted, save the questions for the occasions when you can meet him outside the classroom. Remember that teaching trigonometry is his job, don't be shy and don't be afraid to ask for explanations
Step 4. Continue to solve other practical problems
Complete all the assignments that are assigned, as they are excellent indicators of what the classwork questions will be. If the teacher does not give exercises to do at home, solve the ones proposed in the textbook that refer to the topics of the most recent lesson.
Advice
- Remember that math is a way of thinking and not just a series of formulas to learn.
- Review the concepts of algebra and geometry.
Warnings
- Studying at the last minute for an exam is a technique that rarely works with trigonometry.
- You cannot learn this subject by studying it by heart, you have to understand the related concepts.
