Cos 30 Degrees

The value of cos 30 degrees is 0.8660254. . .. Cos 30 degrees in radians is written as cos (30° × π/180°), i.e., cos (π/6) or cos (0.523598. . .). In this article, we will discuss the methods to find the value of cos 30 degrees 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 Value of Cos 30 Degrees?

The value of cos 30 degrees in decimal is 0.866025403. . .. Cos 30 degrees can also be expressed using the equivalent of the given angle (30 degrees) in radians (0.52359 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (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 between 0° and 90° (First Quadrant). Since cosine function is positive in the first quadrant, thus cos 30° value = √3/2 or 0.8660254. . .
Since the cosine function is a periodic function, we can represent cos 30° as, cos 30 degrees = cos(30° + n × 360°), n ∈ Z.
⇒ cos 30° = cos 390° = cos 750°, and so on.
Note: Since, cosine is an even function, the value of cos(-30°) = cos(30°).

Methods to Find Value of Cos 30 Degrees

The cosine function is positive in the 1st quadrant. The value of cos 30° is given as 0.86602. . .. We can find the value of cos 30 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Cos 30° in Terms of Trigonometric Functions

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

• ± √(1-sin²(30°))
• ± 1/√(1 + tan²(30°))
• ± cot 30°/√(1 + cot²(30°))
• ±√(cosec²(30°) - 1)/cosec 30°
• 1/sec 30°

Note: Since 30° lies in the 1st Quadrant, the final value of cos 30° will be positive.

We can 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 positive x-axis.
• The cos of 30 degrees equals the x-coordinate(0.866) of the point of intersection (0.866, 0.5) of unit circle and r.

Hence the value of cos 30° = x = 0.866 (approx)

☛ Also Check:

• cos 11 degrees
• cos 45 degrees
• cos 180 degrees
• cos 145 degrees
• cos 39 degrees
• cos 115 degrees

FAQs on Cos 30 Degrees

What is Cos 30 Degrees?

Cos 30 degrees is the value of cosine trigonometric function for an angle equal to 30 degrees. The value of cos 30° is √3/2 or 0.866 (approx)

What is the Value of Cos 30 Degrees in Terms of Cot 30°?

We can represent the cosine function in terms of the cotangent function using trig identities, cos 30° can be written as cot 30°/√(1 + cot²(30°)). Here, the value of cot 30° is equal to 1.73205.

How to Find the Value of Cos 30 Degrees?

The value of cos 30 degrees can be calculated by constructing an angle of 30° with the x-axis, and then finding the coordinates of the corresponding point (0.866, 0.5) on the unit circle. The value of cos 30° is equal to the x-coordinate (0.866). ∴ cos 30° = 0.866.

How to Find Cos 30° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 30° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(30°))
• ± 1/√(1 + tan²(30°))
• ± cot 30°/√(1 + cot²(30°))
• ± √(cosec²(30°) - 1)/cosec 30°
• 1/sec 30°

☛ Also check: trigonometric table

What is the Value of Cos 30° in Terms of Cosec 30°?

Since the cosine function can be represented using the cosecant function, we can write cos 30° as [√(cosec²(30°) - 1)/cosec 30°]. The value of cosec 30° is equal to 2.