Value of cos 60
The value of cos 60 is 1/2. Trigonometry is used to study the measurements of right-angled triangles that deals with the parameters such as length, height and angles of the triangle. It has an enormous application in the real world. Apart from Mathematics, it has a wide range of applications in various fields like engineering, architecture, medical imaging, satellite navigation, and the development of sound waves etc. Some applications use the wave pattern of trigonometric functions to produce sound and light waves.
How to derive the value of Cos 60 Degrees?
The value of cos 60 degrees can be represented in terms of different angles like 0°, 90°, 180° and 270° and also with the help of some other trigonometric sine functions. Consider the unit circle in the Cartesian plane. The Cartesian plane is divided into four quadrants. The value of cos 60 takes place in the first quadrant.
Some degree values of sine functions and cosine functions are taken from the trigonometry table to find the value of cos 60 degrees.
We know that
90° – 30° = 60° ———– (1)
From the trigonometry formula,
sin (90° – a) = cos a
We can find the value of cos 60
We can write it as
Sin (90° – 60°) = cos 60°
Sin 30° = cos 60° ——(2)
We know that the value of sin 30 degrees is ½
Now substitute the value in (2)
½ = cos 60°
Therefore, the value of cos 60 degrees is ½
Cos 60° = 1/2
The other values of trigonometric ratios for different angles are given here
Trigonometry Ratio Table | ||||||||
Angles (In Degrees) | 0 | 30 | 45 | 60 | 90 | 180 | 270 | 360 |
Angles (In Radians) | 0 | π/6 | π/4 | π/3 | π/2 | π | 3π/2 | 2π |
sin | 0 | 1/2 | 1/√2 | √3/2 | 1 | 0 | −1 | 0 |
cos | 1 | √3/2 | 1/√2 | 1/2 | 0 | −1 | 0 | 1 |
tan | 0 | 1/√3 | 1 | √3 | Not Defined | 0 | Not Defined | 0 |
cot | Not Defined | √3 | 1 | 1/√3 | 0 | Not Defined | 0 | Not Defined |
cosec | Not Defined | 2 | √2 | 2/√3 | 1 | Not Defined | −1 | Not Defined |
sec | 1 | 2/√3 | √2 | 2 | Not Defined | −1 | Not Defined | 1 |
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Related Links | |
Sin 30 degrees | Cos 0 |
Cos 90 Degrees | value of cos 180 |