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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:
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Trigonometry is used in oceanography, meteorology, seismology, astronomy, physical sciences etc.,
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It is also used to find out the height of tall structures and geographical features, length of a long river, upstream and downstream distance.
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It is used by the aviation industry to measure the speed, direction of the wind to control and fly aircraft and planes
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It is used by archeologists when they excavate new layers of civilization with minimal damage to the area.
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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.
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It is also used to erect walls parallel and perpendicular to each other, build roofs with proper alignment in the construction field
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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
|
Angles in radians |
[0^{circ}] |
[frac{pi}{6}] |
[frac{pi}{4}] |
[frac{pi}{3}] |
[frac{pi}{2}] |
|
sin |
0 |
[frac{1}{2}] |
[frac{sqrt{2}}{2}] |
[frac{sqrt{3}}{2}] |
1 |
|
cos |
1 |
[frac{sqrt{3}}{2}] |
[frac{sqrt{2}}{2}] |
[frac{1}{2}] |
0 |
|
tan |
0 |
[frac{sqrt{3}}{3}] |
1 |
[sqrt{3}] |
Not defined |
|
cosec |
Not defined |
2 |
[sqrt{2}] |
[frac{2sqrt{3}}{3}] |
1 |
|
sec |
1 |
[frac{2sqrt{3}}{3}] |
[sqrt{2}] |
2 |
Not defined |
|
cot |
Not defined |
[sqrt{3}] |
1 |
[frac{sqrt{3}}{3}] |
0 |
Trigonometric Angles in Degrees
|
Angles in radians |
[0^{circ}] |
[30^{circ}] |
[45^{circ}] |
[60^{circ}] |
[90^{circ}] |
|
sin |
0 |
[frac{1}{2}] |
[frac{sqrt{2}}{2}] |
[frac{sqrt{3}}{2}] |
1 |
|
cos |
1 |
[frac{sqrt{3}}{2}] |
[frac{sqrt{2}}{2}] |
[frac{1}{2}] |
0 |
|
tan |
0 |
[frac{sqrt{3}}{3}] |
1 |
[sqrt{3}] |
Not defined |
|
cosec |
Not defined |
2 |
[sqrt{2}] |
[frac{2sqrt{3}}{3}] |
1 |
|
sec |
1 |
[frac{2sqrt{3}}{3}] |
[sqrt{2}] |
2 |
Not defined |
|
cot |
Not defined |
[sqrt{3}] |
1 |
[frac{sqrt{3}}{3}] |
0 |
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.
added soon)
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:
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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
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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.
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The problem given is generally in multiple fractions, try to join it and make a single fraction and start solving it.
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Use the Pythagorean identity to solve the problem easily
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Students should remember when they should apply the double angle formula while solving a problem.