Trigonometry is often considered one of the most important branches of mathematics. It is the study of angles and their relationships to one another, and it has redefined how we understand and study the universe.
Today, most schools and colleges around the world teach trigonometry as a mandatory part of their mathematics curriculum.
But what if you’re not attending school, or would like to learn trigonometry without any outside help? Is it possible to teach yourself such a complex topic?
Yes, you can definitely learn trigonometry by yourself! To do so, there are 4 steps you should follow – understand the basic concepts of geometry, learn about right-angled triangles, memorize important trigonometric formulas, and practice solving a large variety of problems. By following these 4 steps, and with a lot of practice and dedication, you’ll be well on your way to learning trigonometry all by yourself.
In this post, we’ll discuss each of these steps in detail and we’ll even give you some pointers on how you can make your learning experience easier.
Whether you’re preparing for an upcoming trigonometry quiz or just really interested in the subject, we have everything you need.
So, let’s get started!
What Is Trigonometry?
Before learning any topic, it is important that you understand what exactly it’s all about. So, let’s start with the most basic question – what is trigonometry?
Trigonometry is defined as the study of relationships between side lengths and angles of triangles.
This includes topics such as triangle geometry, the Pythagorean theorem, sine, cosine, and tangent functions, and various other identity functions.
The origins of trigonometry can be traced back to the ancient Greek astronomer Hipparchus of Nicaea during 190-120 BC. This makes trigonometry one of the oldest branches of mathematics!
Today, hundreds of scientific disciplines such as physics, engineering, astronomy, architecture, navigation, and even criminology make use of trigonometry.
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4 Steps to Learning Trigonometry by Yourself
Many people believe that learning trigonometry is a herculean task and that it’s next to impossible to do it by yourself.
However, with these 4 steps, you can learn trigonometry at your own pace and in the comfort of your own home.
Step One – Understand the Basic Concepts of Geometry
Geometry is the study of shapes, and trigonometry is the study of a particular shape – the triangle.
This makes trigonometry a subset of geometry. Therefore, the first step toward teaching yourself trigonometry should be to have a strong grasp of the fundamentals of geometry.
This means understanding basic concepts such as points, lines, angles, and shapes. You should also be familiar with more specific terms such as vertices, sides, and altitude.
A good foundation in geometry will make it much easier to understand the different concepts that you’ll come across in trigonometry.
There are many resources available online and in libraries that can help you brush up on your geometry skills.
Here are our recommendations for the best geometry books that you can look up:
- Tutor in a Book’s Geometry by Jo Greig.
- Introduction to Geometry by Coxeter.
- Geometry: Euclid and Beyond by Hartshorne.
Step Two – Learn About Right-Angled Triangles
Now that you have a basic understanding of geometry, it’s time to focus on right-angled triangles.
Trigonometry places a large emphasis on these types of triangles, so it’s important that you understand them inside out.
A right-angled triangle is a type of triangle in which one angle is equal to 90 degrees.
This angle is called the right angle, and the two shorter sides of the triangle are known as the legs. The longer side opposite the right angle is called the hypotenuse.
The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
This theorem is represented by the equation:
a2 + b2 = c2, where a and b are the lengths of the legs, and c is the length of the hypotenuse.
This theorem is one of the most important concepts in trigonometry as it is used to solve many problems involving the sides and angles of right-angled triangles.
A thorough grasp of the Pythagorean theorem will make learning trigonometry much easier.
Step Three – Memorize Important Trigonometric Functions
Trigonometry is all about functions. In mathematics, a function is a rule that assigns a unique output to every input.
There are six main trigonometric functions – sine (sin), cosine (cos), tangent (tan), cosecant (cosec), secant (sec), and cotangent (cot).
Of these, the first three are the most important as they are used most frequently. Let’s take a look at what they mean.
Sine – Ratio of opposite side (of a right-angled triangle) to hypotenuse.
Cosine – Ratio of adjacent side to hypotenuse.
Tangent – Ratio of opposite side to adjacent side.
Cosec, sec, and cotangent are the reciprocals of sine, cosine, and tangent respectively.
To memorize these functions, it might help to think of mnemonic devices. For example, SOH-CAH-TOA (Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent) is a popular one that’s often used to help remember the ratios.
After learning about what these functions mean, you should try and memorize the values for these functions at different angles.
Take a look at the table below.
| Degrees | Radians | sinθ | cosθ | tanθ | cotθ | secθ | cosecθ |
| 0° | 0 | 0 | 1 | 0 | Undefined | 1 | Undefined |
| 30° | π/6 | 1/2 | √3/2 | 1/√3 | √3 | 2/√3 | 2 |
| 45° | π/4 | 1/√2 | 1/√2 | 1 | 1 | √2 | √2 |
| 60° | π/3 | √3/2 | 1/2 | √3 | 1/√3 | 2 | 2/√3 |
| 90° | π/2 | 1 | 0 | Undefined | 0 | Undefined | 1 |
| 180° | π | 0 | -1 | 0 | Undefined | -1 | Undefined |
| 360° | 2π | 0 | 1 | 0 | Undefined | 1 | Undefined |
(θ – Measure of the angle)
Memorizing these values will help you calculate trigonometric problems quite easily.
For e.g., let’s say you want to calculate the hypotenuse of a triangle, and you know one of the angles is 30 degrees and the opposite side is 10 cms.
By using the value of sin(30°), you can easily find the hypotenuse in seconds! (The answer is 20 by the way. Try it for yourself!)
Step Four – Practice Solving A Large Variety of Problems
Now that you understand the basics of trigonometry, it’s time to put your knowledge to the test. The best way to do this is by solving as many problems as possible.
Trigonometry, like all mathematical concepts, requires a lot of practice to master. Some questions will seem easy at first but will become more difficult as you try to solve them.
Don’t get discouraged – just keep practicing and you’ll eventually get the hang of it!
You can find a large number of problems in textbooks and online. We recommend that you start with some easier questions and then gradually move on to the tougher ones.
As you solve more and more problems, you’ll start to develop a feel for how trigonometry works. And pretty soon, you’ll be solving complex problems without breaking a sweat!
Here are our recommendations for the best trigonometry practice books:
The Humongous Book of Trigonometry Problems
This amazing workbook has 750+ problems on trigonometry, covering each and every concept you need to know.
It’s perfect for self-study as it comes with full solutions for every problem. And at just $10, it’s an absolute steal!
Plane Trigonometry by S.L. Loney
Often considered the bible for trigonometry, this classic textbook has been helping students master trigonometry for over a century.
If you’re looking for in-depth coverage of the subject with extensive practice problems and solutions, this is the book for you.
Trigonometry Workbook For Dummies
Possibly the best book for people who want to self-learn trigonometry from the very beginning. It starts with the basics and gradually builds up to more difficult concepts.
There are 100’s of practice problems with step-by-step solutions and even a separate section on how to use trigonometry in everyday life!
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Frequently Asked Questions (FAQs)
Let’s take a quick look at some of the most commonly asked questions regarding learning trigonometry by yourself.
Q.1. How long will it take to learn trigonometry by myself?
A. If you’re starting from scratch, it might take you several weeks (or even longer) to fully understand the core topics of trigonometry.
However, if you already have a strong foundation in mathematics, you should be able to learn the basics of trigonometry within a few days.
Q.2. How many hours per day should I spend on trigonometry?
A. Try to dedicate at least 1-2 hours of focused study time every day. If you can’t find that much time, don’t worry – even 30 minutes of daily practice will help you make steady progress.
Q.3. Is it worth learning trigonometry by myself?
A. Absolutely! Trigonometry is a fascinating subject with many applications in the real world.
Not to mention, it looks great on your resume, especially if you’ve cleared a certification course in trigonometry!
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Final Thoughts
Learning trigonometry by yourself can be a daunting task, but it’s definitely possible. With a little dedication and practice, you’ll be solving complex trigonometric problems in no time!
And the best part? Once you’ve grasped trigonometry, a whole new world of mathematical possibilities will open up for you!
So what are you waiting for? Start learning today!
