Introduction to Trigonometry
Trigonometry is useful for studying the measurements of the right-angled triangles which deal with the parameters like height, length, and angles of a triangle. It has a variety of applications in the real world as well. Apart from Mathematics, it has a huge range of applications in several other fields like engineering, medical imaging, satellite navigation, architecture, development of sound waves, etc. Some applications make use of the wave pattern of the trigonometric functions to produce the light and sound waves.
Trigonometry is a branch of Mathematics dealing with the right-angled triangles. This concept was initiated by the Greek Mathematician Hipparchus. It is further divided into plane Trigonometry and spherical Trigonometry. The cosine function in Trigonometry is used to find out adjacent sides or hypotenuses.
Applications of Trigonometry:
Trigonometry is used in oceanography, meteorology, seismology, astronomy, physical sciences etc.,
It is also used to find out the height of tall structures and geographical features, length of a long river, upstream and downstream distance.
It is used by the aviation industry to measure the speed, direction of the wind to control and fly aircraft and planes
It is used by archeologists when they excavate new layers of civilization with minimal damage to the area.
Trigonometry is used in criminology to measure the collision of objects like cars etc., to understand the case study further. This will help in unveiling the clues further.
It is also used to erect walls parallel and perpendicular to each other, build roofs with proper alignment in the construction field
It is also used in the satellite communication system by drawing imaginary lines between the satellite position, earth center and the destination point to form an imaginary triangle and then measure the dimensions to send the signals exactly through a fixed spectrum.
The table of trigonometric angles will help you to find the values of standard trigonometric angles, including the cos 60 value.
The standard angles of the trigonometric ratios are 0°, 30°, 45°, 60°, 90°.
The values of these trigonometrical ratios of standard angles are essential to solve the trigonometric problems. Hence, it is important to remember the values of the trigonometric ratios of these standard angles. In this article, we would learn about the value of cos 60, how to find the value of cos 60, etc. But before we proceed, let us take a look at the trigonometric angles in the table given below.
Trigonometric Angles in Radians
Trigonometric Angles in Degrees
How to find the Value of Cos 60?
You can represent the value of cos 60 degrees in terms of different angles like 0°, 90°, 180°, 270°. You can also represent it with the help of several other trigonometric sine functions.
Consider the unit circle in a cartesian plane as given below. The cartesian plane can be divided into four quadrants. The cos 60 value in Trigonometry takes place in the first quadrant of the plane.
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Some of the degree values of the sine and cosine functions are taken from the Trigonometry table for finding the value of cos 60.
As you know that 90° – 30° = 60° ...(1)
From the trigonometric formula, sin (90° – a) = cos a
You can now find the value of cos 60.
You can write the above formula as:
Sin (90° – 60°) = cos 60°
This gives you sin 30° = cos 60°...(2)
Since the value of sin 30 is ½,
Substitute this value in (2). Doing so, you get,
½ = cos 60°
Hence, the value of cos 60 degrees is ½.
You can write this as cos 60° = ½
How to improve Scores in Trigonometry
Trigonometry is actually an easy chapter as it deals with only one figure i.e, right- angled triangle. Trigonometric laws are used to determine the unknown values of a right-angled triangle using the known values. Following are some suggestions to solve the trigonometric problems easily and score well:
Try to solve the problem from the complex side. It is easy to solve the complex terms to simple terms by deduction and solving rather than finding out the values of simple terms
To standardize all the terms, try to convert all the values that are in the form of tan, cosec, cot into sin and cos value.
The problem given is generally in multiple fractions, try to join it and make a single fraction and start solving it.
Use the Pythagorean identity to solve the problem easily
Students should remember when they should apply the double angle formula while solving a problem.
FAQs on Value of Cos 60
1. Find the value of cos 60 degree.
If you consider a right-angled triangle, the cosine value of ∠α is the ratio of the length of the adjacent side to the ∠α and its hypotenuse,
where ∠α is the angle that is formed between the adjacent side and the hypotenuse of the right triangle.
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Cosine α = adjacent side / hypotenuse of the triangle
Hence, cos α = b / h
Now, for finding the value of cos 60 degrees, consider an equilateral triangle ABC as shown below.
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In the given triangle, AB = BC = AC.
AD is the perpendicular which is bisecting BC into two equal parts.
As you know, cos α = BD/AB
Consider that these sides have 2 units each:
This means that AB = BC = AC = 2 unit.
Consider that BD = CD = 1 unit.
By using the Pythagoras theorem in the right triangle ABD,
AB2 = AD2 + BD2
Hence, 22 = AD2 + 12
Rearranging and solving, you get, AD2 = 22 -12
= 4 - 1= 3
Therefore, AD = √3
Now, you have got the values of all the sides of triangle ABD.
Hence, the value of cos 60 degree = BD/AB
Cos 60 = ½
2. What is the cos 60 value in fraction?
The cos 60 value in fraction is ½.
Cos 60 = ½
3. What is the value of cos 60 in decimal form?
Since the value of cos 60 degree in fraction is Cos 60 = ½,
The cos 60 value in the decimal form is 0.5.
Cos 60 = 0.5.
4. What is Trigonometry and define the value of cos 60?
Trigonometry is a branch of Mathematics that deals with the angles and sides of a right-angled triangle, helps in finding out the unknown values with the help of known values and trigonometric laws. The concept was developed by the Greek Mathematician Hipparchus. It has huge applications in many fields. It helps in finding out the missing angles and sides in a right-angled triangle with the help of trigonometric laws and formulas. Generally measured angles using Trigonometry are 0, 30, 45, 60, 90 degrees. Trigonometry is further divided into plane Trigonometry and spherical Trigonometry. The trigonometric ratios we find in a triangle are also known as trigonometric functions. Some of the important functions are sine, cosine and tangent. To know more about such functions please refer to the above article on Vedantu. Using the same formula and functions we can determine that the value of cos 60 is ½ in fraction form and 0.5 in decimal form.
5. What are the applications of Trigonometry in real life?
Trigonometry is a subpart of the subject Mathematics. It deals with the angles and sides of a right-angled triangle. It helps in finding out the missing values and unknown values of a right-angled triangle with the help of other known values. Following are the applications of Trigonometry in real - life:
If one knows the value of one side and base of a building, we can find out the height of the building with the help of Trigonometry
It helps in designing games in the IT and gaming industry
Helps in the construction industry to build parallel and perpendicular walls, designing roof inclination, the height of a building, ground surfaces etc.,
Trigonometry is used in the aviation industry to measure the wind speed, distance and direction which helps in flying aircraft and planes.
In physics, Trigonometry is used in measuring field strength, oscillation etc.,
Archeologists also use Trigonometry when they dig up sites and excavate things.
Even in criminology, Trigonometry is used to find out the collision of objects and derive important clues from it.
It also has applications in satellite systems.