Cos 30-degree value is √3/2. The term “trigonometry” deals with the study of the measurements of right-angled triangles with parameters such as length, height and angles of the triangle. The important trigonometric angles are 0, 30, 45, 60, 90, 180, 270 and 360. The angles for six trigonometric functions like sine, cosine, tangent, cosecant, secant and cotangent can be found easily. In this article, let’s discuss the value of cos 30 degrees in detail.
What is Cos 30° Value?
The value of cos 30 degrees in decimals is 0.866 and its value, as a fraction, is √3/2. The derivation of cos 30° is given below.
How to Derive the Value of Cos 30 Degrees?
The value of cos 30 degrees can be found in terms of different trigonometric functions like sine functions and cos functions with varying angles like 60°, 90°, etc., and also with the help of some other trigonometric sine functions. We know that the angle of 30 degrees takes place in the first quadrant of the Cartesian plane; the value of cos 30 degrees should be a positive value.
From the trigonometry table, some degree values of sine functions and cosine functions are used to find the value of cos 30.
We know that
90° – 60° = 30° ———– (1)
From the trigonometry formula,
sin (90° – a) = cos a
We can write,
Sin (90° – 30°) = cos 30°
Sin 60° = cos 30° ——(2)
We know that the value of sin 60 degrees is √3/2
Now substitute the value in (2)
√3/2 = cos 30°
Therefore, the value of cos 30 degrees is √3/2
Cos 30° =√3/2
The trigonometric ratios for different angles and functions are:
| 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/csc | 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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| Also Check: | |
| Sin 30 degrees | Value of cos 60 |
| Cos 90 Degrees | value of cos 180 |
