Cos 30-degree value is √3/2. Trigonometry, the branch of mathematics that deals with the relationships between the angles and the sides of triangles, has several important angles - 0, 30, 45, 60, 90, 180, 270 and 360. The values for these angles can be calculated using the six trigonometric functions - sine, cosine, tangent, cosecant, secant and cotangent. In this article, we will discuss the value of cos 30 degrees in detail.
Value of Cos 30 Degrees - Understanding Trigonometry
Last Updated on Jul 31, 2023
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What is the Value of Cos 30°?
The value of cos 30 degrees is 0.866 in decimal form and √3/2 as a fraction. Let's understand how this value is derived.
How is the Value of Cos 30 Degrees Derived?
The value of cos 30 degrees can be derived using different sine functions and cosine functions with various angles like 60°, 90°, etc. Since 30 degrees lies in the first quadrant of the Cartesian plane, the value of cos 30 degrees will be a positive value.
Using the trigonometry table, we can use the degree values of sine and cosine functions 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 |
For more trigonometric ratio values and mathematics-related content, stay tuned.
| Also Check: | |
| Sin 30 degrees | Value of cos 60 |
| Cos 90 Degrees | value of cos 180 |
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Frequently Asked Questions
What is the value of cos 30 degrees?
The value of cos 30 degrees in decimals is 0.866 and its value, as a fraction, is √3/2.
How is the value of cos 30 degrees derived?
The value of cos 30 degrees can be derived using trigonometric functions like sine and cosine with varying angles like 60°, 90°, etc. Using the formula sin (90° – a) = cos a, we derive cos 30° as √3/2.
What is the value of sin 60 degrees?
The value of sin 60 degrees is √3/2.
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