The worth of **cos 30 levels is 0.8660254. . .You are watching: What is the cosine of 30 degrees**. Cos 30 levels in radians is written as cos (30° × π/180°), i.e., cos (π/6) or cos (0.523598. . .). In this article, we will talk about the techniques to uncover the worth of cos 30 levels with examples.

**Cos 30°:**0.8660254. . .

**Cos 30° in fraction:**√3/2

**Cos (-30 degrees):**0.8660254. . .

**Cos 30° in radians:**cos (π/6) or cos (0.5235987 . . .)

## What is the worth of Cos 30 Degrees?

The value of cos 30 degrees in decimal is 0.866025403. . .. Cos 30 degrees can likewise be expressed making use of the equivalent of the provided angle (30 degrees) in radians (0.52359 . . .)

We know, using level to radian conversion, θ in radians = θ in levels × (pi/180°)⇒ 30 degrees = 30° × (π/180°) rad = π/6 or 0.5235 . . .∴ cos 30° = cos(0.5235) = √3/2 or 0.8660254. . .

**Explanation: **

For cos 30 degrees, the angle 30° lies in between 0° and also 90° (First Quadrant). Since cosine function is optimistic in the first quadrant, thus cos 30° value = √3/2 or 0.8660254. . .Since the cosine duty is a routine function, we have the right to represent cos 30° as, cos 30 levels = cos(30° + n × 360°), n ∈ Z.⇒ cos 30° = cos 390° = cos 750°, and also so on.**Note:** Since, cosine is an also function, the value of cos(-30°) = cos(30°).

## Methods to discover Value the Cos 30 Degrees

The cosine duty is hopeful in the 1st quadrant. The value of cos 30° is offered as 0.86602. . .. Us can find the worth of cos 30 degrees by:

Using Trigonometric FunctionsUsing Unit Circle## Cos 30° in terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 30 levels as:

± √(1-sin²(30°))± 1/√(1 + tan²(30°))± cot 30°/√(1 + cot²(30°))±√(cosec²(30°) - 1)/cosec 30°1/sec 30°Note: due to the fact that 30° lies in the first Quadrant, the last value the cos 30° will certainly be positive.

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We have the right to use trigonometric identities to represent cos 30° as,

-cos(180° - 30°) = -cos 150°-cos(180° + 30°) = -cos 210°sin(90° + 30°) = sin 120°sin(90° - 30°) = sin 60°## Cos 30 degrees Using Unit Circle

To find the value of cos 30 degrees using the unit circle:

Rotate ‘r’ anticlockwise to form 30° angle with the confident x-axis.The cos the 30 degrees equals the x-coordinate(0.866) the the allude of intersection (0.866, 0.5) of unit circle and also r.Hence the value of cos 30° = x = 0.866 (approx)