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.
The table of trigonometrical will help you to find the values of standard trigonometric angles, including the cos 60 value.
The standard angles of the trigonometrical 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 late a look at the trigonometric angles in the table given below.
Angles in radians | \[0^{0}\] | \[\frac{\pi }{6}\] | \[\frac{\pi }{4}\] | \[\frac{\pi }{3}\] | \[\frac{\pi }{2}\] |
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 | \[\sqrt{2}\] | \[\frac{2\sqrt{3}}{3}\] | 1 |
sec | 1 | \[\frac{2\sqrt{3}}{3}\] | \[\sqrt{2}\] | 2 | Not defined |
cot | Not defined | \[\sqrt{3}\] | 1 | \[\frac{\sqrt{3}}{3}\] | 0 |
Angles in degrees | \[0^{0}\] | \[30^{0}\] | \[45^{0}\] | \[60^{0}\] | \[90^{0}\] |
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 | \[\sqrt{2}\] | \[\frac{2\sqrt{3}}{3}\] | 1 |
sec | 1 | \[\frac{2\sqrt{3}}{3}\] | \[\sqrt{2}\] | 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.
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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 trigonometrical 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
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,
AB^{2} = AD^{2} + BD^{2}
Hence, 2^{2} = AD^{2} + 1^{2}
Rearranging and solving, you get, AD^{2} = 2^{2} -1^{2}
= 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.
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