Trigonometry Table – Trigonometric Formula, Ratio and Angle

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Trigonometry is a branch in Science, specifically Mathematics, which deals with the study of the relationship involving the sides and angles of a triangle. It is generally associated with a right-angled triangle, where one of the angles is always 90 degrees.The Trigonometry table by vedantu is drafted in easy manner that can be used to find the values of standard trigonometric angles such as 0°, 30°, 45°, 60° and 90°. It consists of trigonometric ratios – sine, cosine, tangent, cosecant, secant, cotangent (sin, cos, tan, cosec, sec and cot). The values of trigonometric ratios of standard angles are very important to solve the trigonometric problems. Hence, it is important to remember the value of the trigonometric ratios of these standard angles.

Fundamentals of Trigonometric Table

Here is how Trigonometric ratios are calculated for a right-angled triangle :

sin = perpendicular/hypotenuse

cos = base/hypotenuse

tan = perpendicular/base

cot = base/perpendicular (1/tan)

sec = hypotenuse/base (1/cos)

cosec = hypotenuse/perpendicular (1/sin)

Trigonometry Ratio Table
Angles (In Degrees) 30° 45° 60° 90° 180° 270° 360°
Angles (In Radians) π/6 π/4 π/3 π/2 π 3π/2
sin 1/2 1/√2 √3/2 1 -1
cos 1 √3/2 1/√2 1/2 -1 1
tan 1/√3 1 √3
cot √3 1 1/√3
cosec 2 √2 2/√3 1 -1
sec 1 2/√3 √2 2 -1 1

 

Applications of Trigonometric Table

The trigonometric table is essential for navigation, science, astronomy and engineering. This table was effectively used in the pre-digital era, as early as the Egyptian and ancient Greek periods. The table led to the development of the first mechanical computing devices.

The following are some applications of Trigonometry in modern science and everyday life for which it is necessary to know the values of Trigonometry Table.

1. To measure the height of a building or mountains:

If we know the distance from where you observe the building and the angle of elevation you can easily find the height of the building. Similarly, if we have the value of one side and the angle of depression from the top of the building we can find another side in the triangle, all you need to know is one side and angle of the triangle.

2. Trigonometry in construction:

In construction we need trigonometry to calculate the height of the building, the width, length etc according to ratio, and other such things where it becomes necessary to use trigonometry. Architects use trigonometry to calculate structural load, roof slopes, ground surfaces and many other aspects, including sun shading and light angles.

3. Trigonometry in physics

In physics, trigonometry is used to find the components of vectors, model the mechanics of waves (both physical and electromagnetic) and oscillations, sum the strength of fields, and use dot and cross products. Even in projectile motion, we have a lot of application of trigonometry.

4. Trigonometry in archaeology:

Trigonometry is used to divide the excavation sites properly into equal areas of work. Archaeologists identify different tools used by civilization, using trigonometry can help us in these excavations. We can also use it to measure the distance from underground water systems.

5. Trigonometry in criminology:

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, or in which angle was a bullet shot etc.

6. Trigonometry in marine biology:

Marine biologists often use trigonometry to establish measurements. For example, to find out how light levels at different depths affect the ability of algae to photosynthesize. Trigonometry is used in finding the distance between celestial bodies. Also, marine biologists utilize mathematical models to measure and understand sea animals and their behaviour. Marine biologists may use trigonometry to determine the size of wild animals from a distance.

7. Trigonometry in marine engineering: 

In marine engineering, trigonometry is used to build and navigate marine vessels. To be more specific trigonometry is used to design the Marine ramp, which is a sloping surface to connect lower and higher-level areas, it can be a slope or even a staircase depending on its application.

Trigonometry is used to set directions such as the north-south and east-west, it tells you what direction to take with the compass to find out exact direction. Trigonometry has many uses, this is just the beginning! 

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