What is the Value of Cos 30 Degrees?

The value of cos 30 degrees in decimals is 0.8660. Converting degree to radian, that is, θ in radians = θ × π/180° or θ × Pi/180°. Therefore, converting cos 30° in radians will give cos (30 × π/180°), and the final value in radians will become cos(π/6) or cos (0.5235). Following are the values of cos 30° in different forms,

  • Cos 30° in decimal = 0.8660
  • Cos 30° in radians = cos(π/6) or cos (0.5235)
  • Cos 30° in fraction = √3/2
  • Cos (-30°) = 0.8660

Cos 30 Degrees

Cos 30 Degrees: The value of cos 30 degrees in trigonometry is √3/2. In a right-angled triangle, cosine is the ratio of the base and hypotenuse. When the angle of the right-angled triangle is 30°, cos 30° is required. In fraction form, cos 30° is √3/2; in decimal form, the value is 0.8660.

Let’s understand how the value of cos 30° is obtained with examples.

Table of Content

  • What is the Value of Cos 30 Degrees?
  • How to Find the Value of Cos 30 Degrees
  • Cos 30 Degrees – Methods to Find
    • Cos 30 Degrees in Terms of Trigonometric Functions
    • Cos 30 Degrees Using Unit Circle
  • Cos 30 Degrees Proof
    • Theoretical Approach
    • Practical Approach
    • People Also Read:
  • Solved Examples on Cos 30 Degrees

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What is the Value of Cos 30 Degrees?

The value of cos 30 degrees in decimals is 0.8660. Converting degree to radian, that is, θ in radians = θ × π/180° or θ × Pi/180°. Therefore, converting cos 30° in radians will give cos (30 × π/180°), and the final value in radians will become cos(π/6) or cos (0.5235). Following are the values of cos 30° in different forms,...

How to Find the Value of Cos 30 Degrees?

In order to find the value of cos 30 degrees, the unit circle is taken into account. While looking at the unit circle, it is noticed that the value of cos 30° in the first quadrant is positive and is given as 0.8660. There are two ways to find out the value of cos 30°. The methods are mentioned below:...

Cos 30 Degrees – Methods to Find

Cos 30 Degrees in Terms of Trigonometric Functions...

Cos 30 Degrees Proof

There are two approaches to deriving the value of cos 30 degrees, they are:...

Conclusion

Cos 30 degrees is important in both math and real-world applications. The value of cos 30 degrees is √3/2, and it helps us solve problems involving right triangles, trigonometric functions, and various calculations in physics and engineering. By knowing this fundamental trigonometric value, we can easily tackle many problems and gain a deeper appreciation for the role of trigonometry in our daily lives....

Solved Examples on Cos 30 Degrees

Example 1: In a right-angled triangle, the base to the angle of 30° is 9m. Find the length of the Hypotenuse....

Practice Problems on Cos 30 Degrees

Problem 1: Evaluate 5⋅cos(30°)+3....

Cos 30 Degrees – FAQs

What is the value of cos 30° in terms of cot 30°?...