Trigonometry is a branch of mathematics that studies triangles and circles. Trigonometric functions are used to describe the properties of angles, relationships in triangles, and graphs of repeated cycles. Learning trigonometry will help you understand, as well as visualize and graph these relations and cycles. If you combine self-study with staying focused in class, you will understand the basic concepts of trigonometry and may begin to understand the circles in the world around you.
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Method 1 of 4: Focusing on Trigonometry Fundamentals
Step 1. Determine the parts of a triangle
In essence, trigonometry is the study of the relationships that exist in triangles. A triangle has three sides and three angles. By definition, the sum of the angles of any triangle is 180 degrees. You will need to familiarize yourself with triangles and their terms to be successful in trigonometry. Some common terms for triangles are:
- Hypotenuse The longest side of the triangle.
- Obtuse angle An angle that is greater than 90 degrees.
- Acute angle An angle that is less than 90 degrees.
Step 2. Learn to make a unit circle
The unit circle lets you scale any triangle so that its hypotenuse is equal to one. This concept is useful in relating trigonometric functions, such as sine and cosine, to percents. Once you understand the unit circle, you can use trigonometric values for certain angles to answer questions about triangles that have those angles.
- Example 1: The sine of a 30-degree angle is 0.50. That is, the side opposite the 30-degree angle is half the length of the hypotenuse.
- Example 2: This relation can be used to find the length of the hypotenuse of a triangle that has an angle of 30 degrees and the length of the side opposite that angle is 18 cm. The hypotenuse is 36 cm.
Step 3. Understand trigonometric functions
There are six central functions in understanding trigonometry. Taken together, these six functions define the relationship in a triangle, and allow you to understand the unique properties of any triangle. The six functions are:
- Sine (Sine)
- Cosine (Cos)
- Tangent (Tan)
- Secan (Sec)
- Cosecant (Csc)
- Cotangent (Cot)
Step 4. Understand the relation of trigonometric functions
One of the most important things to understand about trigonometry is that all the functions are related. Although the values of sine, cosine, tangent, etc., have their own uses. The most important benefit is the relationship between all these functions. The concept of a unit circle makes the relation easier to understand. Once you understand the unit circle, you can use the relations described by the unit circle to create models for other problems.
Method 2 of 4: Understanding the Application of Trigonometry
Step 1. Understand the basic use of trigonometry in an academic context
Apart from learning trigonometry for fun, mathematicians and scientists actually apply this concept. Trigonometry can be used to find the value of angles or line segments. You can also explain cyclical behavior by describing it as a trigonometric function.
For example, the motion of a spring bouncing back and forth can be described by describing it as a sine wave
Step 2. Think about cycles in nature
Sometimes, people have difficulty understanding abstract concepts in math or science. If you notice that these concepts exist in the world around you, you will often see them from a new perspective. Look for objects around you that move cyclically, then try to relate them to trigonometric concepts.
The Moon has a predictable cycle of approximately 29.5 days
Step 3. Visualize how to study natural cycles
Once you realize that nature is full of cycles, start thinking about ways to study it. Think about a graphic model to describe such a cycle. From the graph, you can formulate an equation to explain the observed phenomenon. Furthermore, trigonometric functions will have meaning to help you understand their benefits.
Imagine you are measuring waves on a beach. During high tide, the wave will reach a certain height. Then, the wave will recede until it reaches a certain point. From low tide, the water will rise again to the beach until it reaches a height at high tide. This cycle will go on without end, and can be described as a trigonometric function, for example as a cosine wave
Method 3 of 4: Studying Early
Step 1. Read the trigonometry chapter
For some people, the concepts of trigonometry are difficult to understand at first. If you read the trigonometry chapter before it is taught in class, you will be more familiar with the material. The more often you look at the material, the more connections you can make about the relationships between the different concepts in trigonometry.
It also allows you to identify trigonometric concepts before we run into trouble in class
Step 2. Use a notebook
Reading a book quickly is better than nothing. However, it will be more helpful for you to learn trigonometry by reading further. Keep detailed notes about the chapter you are currently reading. Remember that trigonometry is a cumulative concept and supports each other. It's great if you have notes from the previous chapter because it will help you in understanding the current chapter.
Also write down any questions you want to ask your teacher
Step 3. Work on the problems from the book
Some people can visualize trigonometric concepts well, but you also have to answer questions. To make sure that you really understand the material, try doing some questions before going to class. That way, you'll know exactly what help you need in class if you're having trouble.
Most books have an answer key on the back. You can check your answer
Step 4. Bring trigonometry material to class
By taking notes and practicing questions to class, you will have a point of reference. That way, you can recall everything you have understood, as well as remember all the concepts that still require further explanation. Be sure to ask all the questions you write down while reading.
Method 4 of 4: Taking Notes in Class
Step 1. Write in the same notebook
All trigonometric concepts are interconnected. It's best practice to record everything in the same notebook so you can refer back to previous notes. For that, prepare a notebook or special binder for your trigonometry lessons.
You can also continue to practice working on the questions in this book
Step 2. Prioritize trigonometry lessons
Avoid wasting time in class socializing or catching up on homework for other subjects. When you are taking trigonometry lessons, you have to focus on face-to-face and practice questions. Write all the teacher's notes on the blackboard or whatever is important.
Step 3. Get involved in teaching and learning activities
Volunteer to answer the questions on the board, or submit your answers for practice questions. Ask questions if something is not understood. Communicate openly and smoothly with your teacher. All of these things will help you learn and enjoy trigonometry.
If your teacher prefers not to be interrupted during a lesson, save your questions to ask after class. Remember that the teacher's job is to help you learn trigonometry. So, don't be shy
Step 4. Continue your efforts by doing more questions
Complete all given homework. Homework questions are a good guide to exam questions. Make sure you understand each question. If your teacher doesn't give homework, try to do the questions containing the concepts presented at the last meeting in your book.
Tips
- Remember that mathematics is a way of thinking, not just a collection of formulas to be memorized.
- Re-learn algebraic and geometric concepts.
Warning
- You can't learn trigonometry by forcing yourself to memorize. You have to understand the concepts.
- It is rare for anyone to successfully pass a trigonometry exam just by cramming in material all night.
