Introducing the world of trigonometry
Trigonometry is one of the oldest and widely used branches of mathematics. It is interesting how many cultures came to the same conclusions and how many parallels can be drawn between their notes. The study of trigonometry started around 2nd millennium BC in Egypt and Mesopotamia. Firstly, trigonometry wasn’t considered math at all, but a calculation tool. The trigonometry we know now didn’t show until 18th century. Egyptians developed trigonometry from measuring land and building pyramids. While Egyptians were builders, Mesopotamians were astronomers and mostly developed their knowledge in trigonometry trying to calculate distance and mapping the stars and planets.
We can find trigonometry in almost every aspect of our lives, which is why it isn’t that hard to picture it and learn it. First thing you should learn is some basic trigonometric ratios in a right triangle. You’ll learn about sine, cosine, tangent and cotangent and some of their uses. This introduction will lay some grounds for you to learn more and more. Even after one small lesson you’ll be able to calculate so many real life problems with little effort.
Whether you are a beginner and want to start learning about trigonometry, or you simply want to learn more, we have what you need!
The main Pythagorean identity is the notation of Pythagorean Theorem in made in terms of unit circle, and a specific angle.
Trigonometric equations are equations that come in form f(x) = a where a is a real number, and f(x) some trigonometric function.
What is unit circle, where is unit of trigonometric function placed on circle and find special angles in trig.
Trigonometry is important part of geometry that includes calculation of sine, cosine, tangent, cotangent, etc.
Proofs made easy
Pythagoras was ancient Greek mathematician. He made an incredible discovery about triangles. The legend has it that one day he was very, very bored and as he stared at the tiles on the floor he started noticing a curious pattern. The tiles were in the shape of isosceles triangles. Here he noticed a very important relation between sides of a triangle. He came to his famous Pythagorean Theorem. This idea evolved, and after some time, the great Pythagorean Theorem got a new notation which is called the main Pythagorean identity. Soon enough, two more identities developed. People recognized how important this is and kept on researching.
As people researched, many new formulas accrued. Now we know formulas for angle addition, law of cosines and law of sines, many trigonometric identities and product and sum identities. This all makes proving trigonometric theorems very easy because we can use so many statements we know are true. You can learn everything about this here.
This is how, from one boring day and extraordinary mind, one great branch of geometry was born.
Looking at things from a different angle
When you already get aquatinted with angles and trigonometric functions we’ll show you what they actually represent on a unit circle. You will learn another way of looking at angles and how to find them if you know only their sine, cosine, tangent or cotangent value, what is the easiest way to draw them and how to memorize things you’ll need. Don’t worry if this sounds a bit complicated, we provided you with many examples you can follow so you can do everything on your own soon enough. If some things are hard for you to learn by heart, we’ll always find a way to make it easier for you. You’ll find out what are the most common special angles and why are they so important to us.
So, get your compass and pencil in your hands, open the lessons and start learning.
Missing equations and inequalities?
Now to worry, there are plenty tasks and problems in trigonometry that include equations and inequalities. Don’t start panicking, we got you covered. Everything you need you can find in these lessons. We won’t lie, this part isn’t that easy and it requires work, but with a little bit of your time and dedication you’ll have no problem with mastering this field. There are more than one type of trigonometric equation, and there are more than one way to solve them. We solved and explained every type of a problem you may encounter in your trigonometric journey.
Why is trigonometry so important?
Even though you may not like math it is very likely you’ll have to use trigonometry in whatever you do. Starting from the simple life problems we explained to the real complicated ones, trigonometry is everywhere. In economy, especially statistics, architecture, astronomy, geology, art and many more. Trigonometry is also used to prove many theorems and lemmas, which means that many sciences that exist today would not exist if it wasn’t for trigonometry. Think of just how many things we would miss out- no pyramids, no modern buildings, and technology.
All this knowledge is within your reach. All you need is a good start.