Post on Applications of Trigonometry

Hello everyone,

I am Ajinkya Naik .I am a Science student and this blogpost has been originated due to one of our assignments. ;) and that too a Maths one :o. Usually when someone says “MATHS”,we are like.. 

But Maths is a part of our lives, whether we clean the house or go shopping. It’salmost impossible to get through a day without using maths in some way, because our world is full of numbers to handle and problems to solve. Wherever you go, whatever you do, you are using maths daily without even realizing it.

It just comes naturally.

So here is my first blog post dedicated to one of the most important branches of Mathematics, Trigonometry.

What is Trigonometry?

Trigonometry is a branch of mathematics that studies relationships involving lengths and angles of triangles. It was emerged in the third century BC involving applications from astronomy to geometric studies. Apart from these two, technology fields that use trigonometric  concepts include Navigation, Optics, Acoustics ,Electronics,Statistics,Number theory, Electrical engineering, Mechanical engineering, computer graphics, Game development, Civil engineering, Medical imaging, Pharmacy, Cartography (creating maps),Seismology ,Crystallography .

Applications of Trigonometry

Historical uses of trigonometry (in a nutshell)

Trigonometry was initially used in astronomy. Before the sixteenth century, the subject of astronomy was based completely on the concept that Earth is placed in the center of a number of nested spheres. Therefore, it can be said that trigonometry was mainly used for calculating the positions of planets and stars.

Trigonometry is also of paramount importance in daily life. I am mentioning few of the applications here:

1)  To Measure Height of a building or a mountain; distance from a place; construction

Trigonometry is used to in measuring the height of a building or a mountain. The distance of a building from the viewpoint and the elevation angle can easily determine the height of a building using the trigonometric functions. Architects use trigonometry to calculate structural load, ground surfaces and many other aspects, including sun shading and light angles, making parallel and perpendicular walls, installing ceramic tiles and roof inclination.

Fig1.1

Fig 1.2  

2) Aviation

Fig 2.1

The aviation technology has been evolved in many up-gradations in the last few years. Flight engineers have to take in account their speed, distance, and direction along with the speed and direction of the wind. Trigonometry allows pilots and flight engineers to account for their speed, velocity, angle of ascent or descent, as well as other external factors such as wind speed and direction. To do this, they utilize triangles and other structures composed of vectors. Computations involving these vectors allow them to solve complex problems and accurately model the behavior of their vehicles and environments.

Many pilots are also trained in the use of on-the-spot trigonometry to come up with quick estimates of their location and positioning in the air space. Usually, these calculations are based on the angle and position of the sun relative to a pilot's plane. 

3) Criminology

It is used to identify how an object falls or in what angle the gun is shot.(May be Dr.Salunkhe from C.I.D. used trigonometry. Who knew? :o)

In criminology, trigonometry can help to calculate a projectile’s trajectory, to estimate what might have caused a collision in a car accident or how did an object fall down from somewhere.

                                                              Fig 3.1

Suppose an old man fell off a ledge of a building in an apparent suicide, with a suicide note and everything. The impact marks on the ground where the man fell are abnormal for someone his age. This suggests that the speed of the man when he fell was also highly abnormal, with the rate of increase in speed not making sense for someone so old and with barely enough power to jump off the ledge. Not only that, the distance he flew from the edge of the building into the open air is also abnormal for someone such as himself. By using the distance between the ledge of the building and where the man fell as one “leg” and the distance from the ledge to the ground as another, with respect to the speed of the man as he continued to fall, crime scene investigators could use the Pythagorean Theorem, effectively turning a “hunch” into probable cause: upon use of this trigonometric formula, it is mathematically proven that the man couldn’t have pushed himself that far off the ledge, and wouldn’t have fallen at as high a speed as he did. Instead of an apparent suicide, crime scene investigators now have a reasonable suspicion that the man was murdered: someone pushed him off the building, since it’s mathematically proven that he simply couldn’t have done it himself.

4) Marine Biology

Marine biology is the study of species inhabiting the oceans and other saline aquatic environments, and the way in which these organisms interact within their habitats. Trigonometry is often used by marine biologists for measurements to figure out the depth of sunlight that affects algae to photosynthesis. Using the trigonometric function and mathematical models, marine biologists estimate the size of larger animals like whales and also understand their behaviors.

  

Fig 4.1

5) Oceanography

Trigonometry is used in oceanography to calculate heights of waves and tides in oceans. For example, if the oceanographer was tracking a sea creature and they needed to know how far away they were from the creature,(as far away as possible if you ask me!) they would use trigonometry to find out the distance from them and the creature.

A semidiurnal tide is a body of water,  like the Atlantic Ocean, that has two high tides and two low tides each and every day because tides behave the same way in a given period. An Oceanographer would use trigonometry to plot a graph showing the size of the tide at each time of day - high and low tide.

Fig 5.1

6) Navigation

Navigation is the process to accurately determine one’s position and planning a route for the movement of a craft or vehicle from one place to another.

Trigonometry is fundamental to navigation. Trigonometry is used extensively in calculations referring to Cartesian coordinates. Cartesian coordinates are used to represent North, South, East and West directions. Trigonometry is used in navigating directions using Compass; it estimates in what direction to place the compass to get a straight direction. With the help of a compass and trigonometric functions in navigation, it will help to pinpoint a location and also to find distance as well to see the horizon. It used in creation of maps too.

Spherical Trigonometry:It is the branch of trigonometry concerned with the measurement of the angles and sides of spherical triangles.It is used for planning long distance routes around the world. This form of trigonometry helps get to a location faster.

Fig 6.1

7) Astronomy

In ancient times , the  astronomers kept detailed records on the rising and setting of stars, the motion of the planets, and the solar and lunar eclipses, all of which required familiarity with angular distances measured on the celestial sphere. Trigonometry is mainly used to measure the distance to stars in the solar system ,the motion of nearby stars compared to more distant stars, the distance from one planet to another, and the distance between other spherical objects. The method of measuring distance in space is called trigonometric parallax.

Fig 7.1

8) Video Games

Maths is everything when it comes to games. From having the ability to calculating the trajectory of an Angry Bird flying through the sky, to ensuring that a character can jump and come back down to the ground -- without the help of mathematics, games simply wouldn't work. Trigonometry is used a lot in game development, from calculating the distance/angle between two objects to calculating the appropriate trajectory after a collision.

A character wouldn't be able to walk up a slope, slide down a slide, fire a bullet from a gun, or even jump without the help of the mathematics.

In graphics , it's used in lighting calculations to determine the amount of light using the cosine of the angle between the normal and the light direction. It is used in bump mapping when calculating the angles between the eye vector, normal and light direction   

Fig 8.1

In case you don’t know :

Acoustics :The science of studying mechanical waves in solids, liquids and gases that also topics like sound, infrasound, ultrasound and vibration.

Seismology :Science of studying earthquakes

Crystallography :The study of atom arrangements in a crystalline solid.

Cartography :creating maps

Trigonometric parallax :When an object is seen from two different vantage points, the object appears to change positions compared to the background objects. For instance, when you place your finger in front of your face and look at it with your left eye then your right eye, the position of your finger appears to change compared to the distant objects in the background. The effect is called parallax, or trigonometric parallax in astronomy.

I hope you liked the post.Do share your feedback.Thank you!

Sites referred:

https://www.quora.com/How-is-math-used-in-video-game-designing-and-programming

https://trigonometryinastronomy.wikispaces.com/Applications+of+Trigonometry+in+Astronomy

https://allabouttrig.wordpress.com/navigation/

and many more...