# What is trigonometry?

Trigonometry is the area of mathematics dealing with the study and measure of triangles, the relationships between their angles and sides, and the trigonometric functions of sine, cosine, tangent, cotangent, secant, and cosecant.

This mathematical branch is related to other scientific areas directly and indirectly, and it applies to everything that requires precision measurements, such as spatial geometry and astronomy, for measuring the distances between stars with respect to other geographical points.

The study of trigonometry has existed for more than three thousand years. In Babylon and Egypt, the measurements for triangles’ angles were used to build pyramids.

## What is the importance of trigonometry?

The application of trigonometric functions in physics, astronomy, telecommunications, nautical fields, engineering, cartography, and others is what makes them significant: they allow you to calculate distances accurately without necessarily having to travel them.

Knowing this, the importance of trigonometry lies in the various applications it has in the following examples:

• Calculating the distance between two points where one, or even both, are inaccessible.
• Accurately calculating distances and angles of inclination, which is very useful for civil engineering.
• Calculating the height of a point that may also be inaccessible.

## What are the units of measurement in trigonometry?

When studying the measurement of angles, as well as their calculation, trigonometry uses the following units:

1. Radian: basic angular unit in trigonometry that indicates the relationship that exists between the angle formed based on the radius of a circumference and an arc of the same length. A full circle is made up of two radians.
2. Sexagesimal degree: angular unit that divides a circumference into 360 degrees, considering that each right angle has 90 degrees, and if the circumference is divided into four equal parts, the sum of each angle will give a total of 360. It is usually used in the practical field of branches such as engineering, architecture, or physics.
3. Centesimal degree: an angular unit that divides a circumference into 400 centesimal degrees.
4. Milliradian: a unit that divides the circumference into 6,400 units.

## What are the trigonometric functions?

Trigonometric functions are the metric ratios between the sides of a right triangle. For a triangle that has a right angle of 90 degrees, three fundamental elements can be determined:

1. Angles: the area of the plane that lies between two semi-straight lines with a common origin. This is the amplitude of the arc of a circle, with its center at the vertex and bounded by its sides.
2. Legs: the other sides that make up a triangle. They can be classified into the opposite leg (which is located on the opposite side or in front of the angle in question) and adjacent (which is located next to the angle in question).
3. Hypotenuse: the longest side of a triangle that is opposite the right angle.

Understanding these three fundamental concepts, the trigonometric functions are:

• Sine: the ratio between the opposite leg of the angle in question and the hypotenuse.
• Cosine: division of the adjacent leg of the angle in question by the hypotenuse of the triangle.
• Tangent: ration between the opposite side and the adjacent leg of the triangle. It is expressed as sine over cosine.

Every trigonometric function has its reciprocal ratio, i.e.:

• Secant: reciprocal ratio of the cosine consisting of the ratio between the length of the hypotenuse and the length of the adjacent leg.
• Cosecant: reciprocal ratio of the sine consisting of the ratio between the length of the hypotenuse and the length of the opposite leg.
• Cotangent: reciprocal ratio of the tangent consisting of the ratio between the length of the adjacent leg and that of the opposite one.