What is Trigonometry?

Trigonometry is certainly one of the most important branches of Mathematics which we must pay close attention to if we aim to have a career in astronomy, navigation, surveying, geodesy, architecture, electronics, meteorology, oceanography, crystallography, video games, and all those cool professions which we mainly see on documentary channels.

We have to bear in mind that is not an easy topic, considering that it is known for its many identities, but yet it is not something to be scared of and run from, as it is a very lovely subject and easy to navigate through.

Let’s begin with its meaning: Trigonometry is a Greek word – the first part of the word “trigon” means “triangle”, whereas the second part of the word “metron” means “a measure”. As it can be understood from its meaning, trigonometry was used to measure angles and sides of a triangle.

The main functions in trigonometry are sine (sin), cosine (cos), and tangent (tan). They are one side of a right-angled triangle divided by another side:

Sin A = opposite/hypotenuse = a/c

Cos A = adjacent/hypotenuse = b/c

Tan A = opposite/adjacent = a/b

The reciprocals of these functions are: cosecant (csc), secant (sec), cotangent (cot).

Csc A = 1/Sin A = hypotenuse/opposite = c/a

Sec A = 1/Cos A = hypotenuse/adjacent = b/c

Cot A = 1/Tan A = adjacent/opposite = Cos A/Sin A = b/a

Any question regarding arbitrary triangles can be answered by using the law of cosines and the law of sines.

Another way to represent trigonometric functions is by using the unit circle, which is a circle with a radius of 1. Because of this, we can measure sine, cosine and tangent. Placed in a standard position, the terminal side of an angle A will intersect in a unit circle in a point (x,y), where x = cos A, and y = sin A. Thus, we will be able to calculate trigonometric values such as:

It is very clear that by this blog we will not be able to make justice to this topic. However, these are the most important elements of trigonometry which will certainly help you in solving any question dealing with arbitrary triangles.