Trigonometry is one of the most important concepts in the subject of mathematics. It basically deals with the right-angled triangle in which we study the various relationships between the angles and the sides of the right-angled triangle. Have you ever wondered how we measure the height of mountains like Mount Everest or Mount Kailash? Do we go to these mountains to measure their height? No. We took the help of the concept of trigonometry to find out the height of these gigantic mountains.
We have several other innumerable applications of the concept of trigonometry in our real life. In this article, we will discuss the various types of trigonometry along with its important real-life applications but before that, let us understand the trigonometry table.
Trigonometry Table
Trigonometry table provides us with all the necessary values of the various trigonometry ratios. This table helps us to understand and learn various values of the trigonometric ratios effectively and efficiently. The trigonometry table for the value of trigonometric ratios starting from 0 degrees to 360 degrees is given below:
| Angle in degrees | sine | cosine | tangent | cosecant | secant | cotangent |
| 0 degrees | 0 | 1 | 0 | Not defined | 1 | Not defined |
| 30 degrees | 1/2 | √3/2 | 1/√3 | 2 | 2/√3 | √3 |
| 45 degrees | 1/√2 | 1/√2 | 1 | √2 | √2 | 1 |
| 60 degrees | √3/2 | 1/2 | √3 | 2/√3 | 2 | 1/√3 |
| 90 degrees | 1 | 0 | Not defined | 1 | Not defined | 0 |
| 180 degrees | 0 | -1 | 0 | Not defined | -1 | Not defined |
| 270 degrees | -1 | 0 | Not defined | -1 | Not defined | 0 |
| 360 degrees | 0 | 1 | 1 | Not defined | 1 | Not defined |
Various Types of Trigonometry
Trigonometry is categorized broadly in four types which are as follows:
- Core Trigonometry: It is that type of trigonometry which deals with the core concept which means it deals with the relationship between the angles and the sides of a right-angled triangle. The presence of a triangle that has one angle equivalent to 90 degrees is imperative in core trigonometry. This type of trigonometry is taught in the higher classes and in colleges.
- Plane Trigonometry: To find out the distances and the height of the angles in a plane triangle, we take the help of plane trigonometry. This type of trigonometry is used by architects, physicists, mechanical engineers, chemists, and so on.
- Spherical Trigonometry: This type of trigonometry deals with those triangles that are drawn on a three-dimensional geometrical figure called a sphere. Spherical trigonometry originated in the 8th century where it was used to determine the positions of sunsets and sunrises. Today, it is widely used by scientists and astronomers to study the various distances within our universe. There are also many navigators and mapmakers across the world who use spherical trigonometry.
- Analytic Trigonometry: It can be classified as the subset of core trigonometry. Analytic trigonometry seeks to determine various values based on the x-y plane of various triangles. The concept of analytic trigonometry is used in the field of science and engineering.
Various Real-life Applications of Trigonometry
- The concept of trigonometry is used broadly in the field of astronomy. Many reputed institutions like NASA, ISRO, and so on use trigonometry for various purposes like measurement of the distance between stars and Earth, etc. Without trigonometry, we could never have made it to the moon.
- Navigation and aviation use trigonometry.
- Crime investigators use trigonometry to deduce many conclusions in a crime scene.
- Trigonometry is also used widely in the field of pharmacy and medical imaging. Various techniques like ultrasound, imaging, nuclear medicine, etc used the concept of trigonometry.
- Along with the field that we discussed above, trigonometry is also used in the field of optics, engineering, game development, computer graphics, cartography, and so on.
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