# Applications of Trigonometric Functions

Trigonometric functions are functions of an angle or an abstract quantity used in trigonometry. These functions include sine, cosine, tangent, cosecant, secant, and cotangent. Trigonometric functions have a wide variety of applications in different areas such as engineering, science, architecture, and construction.

In this article, we will look at some of the applications of the most important trigonometric functions.

##### ALGEBRA

Relevant for

Learning about various applications of trigonometric functions.

See applications

##### ALGEBRA

Relevant for

Learning about various applications of trigonometric functions.

See applications

## Are there applications of trigonometric functions in everyday life?

Trigonometric functions have a wide variety of applications in everyday life. Although we do not find trigonometric functions directly in our day to day, these functions are used in many of the things we use every day, such as music.

We know that sound travels through waves and this pattern, although not as regular as a sine or cosine function, is very useful for computer music processing.

A computer obviously cannot hear and understand music in the same way that we do, so computers represent this mathematically by their constituent waves.

This means that sound engineers need an understanding of trigonometric functions. Thanks to trigonometry, we can listen to the music that we love so much every day.

## Applications of trigonometric functions in engineering

Aviation and aeronautical engineering: In aviation, engineers have to take into account their speed, distance, and the direction of both their own speed and the wind speed.

The wind plays a very important role in how and when a plane will land and when it is necessary, this is solved by using vectors to create a triangle and using trigonometric functions to solve.

For example, if the plane is traveling at 500 km/h at 45° north of east, and the wind is traveling from north to south at 30 km/h, the trigonometric functions can be used to solve and find the third side of the triangle, which will indicate the correct direction.

Satellites: Trigonometric functions are also used in satellites. The location of the satellite and its angles can be measured with trigonometric functions. The position or exact location of the satellite can be measured using trigonometric ratios.

Naval engineering: Trigonometric functions are used in naval engineering to build and navigate marine vessels. To be more precise, the trigonometric functions are used to design the marine ramp, which is an inclined surface that serves to connect low-level areas with high-level areas. This ramp can be a slope or even steps depending on the application.

Video game engineering: You may have played Mario. When he jumps, he doesn’t actually jump in a straight line on the y-axis but instead jumps in a parabolic curve. Trigonometric functions help Mario jump over obstacles.

## Applications of trigonometric functions in architecture and construction

Trigonometric functions are widely used in architecture and construction. Architects use trigonometry to calculate different aspects of buildings such as roof slopes, light angles, structural loads, and surfaces, among others.

In construction, trigonometric functions can be used to measure fields, lots, and areas. They can also be used to build parallel walls and perpendicular structures. Precise ceramic installation also uses these functions. There are many other things where trigonometry becomes essential, especially when it is necessary to measure angles and calculate distances.

## Applications of trigonometric functions in science

Physics: In physics, trigonometric functions are used to find the components of vectors, model the mechanics of both physical and electromagnetic waves and oscillations. The sum of the field strength, the dot and cross products, and even the parabolic motion are based on the trigonometric functions.

Archeology: Trigonometry is used to properly divide excavation sites into equal work areas. Trigonometric functions can be useful in excavations. In addition, they can also be used to measure the distance of underground water systems.

Criminology: In criminology, trigonometric functions can be used to calculate parabolic trajectories or other types of motion. For example, you can estimate what caused a car to crash or the angle at which a bullet was fired.

Marine Biology: Marine biologists use trigonometric functions frequently. For example, it is possible to estimate how light levels at different depths affect the algae’s ability to photosynthesize. Marine biologists may also use mathematical models to measure and understand marine animals and their behavior. For example, it is possible to determine the size of animals from a distance.  