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Cos pi/6
The value of cos pi/6 is 0.8660254. . .. Cos pi/6 radians in degrees is written as cos ((π/6) × 180°/π), i.e., cos (30°). In this article, we will discuss the methods to find the value of cos pi/6 with examples.
 Cos pi/6: √3/2
 Cos pi/6 in decimal: 0.8660254. . .
 Cos (pi/6): 0.8660254. . . or √3/2
 Cos pi/6 in degrees: cos (30°)
What is the Value of Cos pi/6?
The value of cos pi/6 in decimal is 0.866025403. . .. Cos pi/6 can also be expressed using the equivalent of the given angle (pi/6) in degrees (30°).
We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)
⇒ pi/6 radians = pi/6 × (180°/pi) = 30° or 30 degrees
∴ cos pi/6 = cos π/6 = cos(30°) = √3/2 or 0.8660254. . .
Explanation:
For cos pi/6, the angle pi/6 lies between 0 and pi/2 (First Quadrant). Since cosine function is positive in the first quadrant, thus cos pi/6 value = √3/2 or 0.8660254. . .
Since the cosine function is a periodic function, we can represent cos pi/6 as, cos pi/6 = cos(pi/6 + n × 2pi), n ∈ Z.
⇒ cos pi/6 = cos 13pi/6 = cos 25pi/6 , and so on.
Note: Since, cosine is an even function, the value of cos(pi/6) = cos(pi/6).
Methods to Find Value of Cos pi/6
The cosine function is positive in the 1st quadrant. The value of cos pi/6 is given as 0.86602. . .. We can find the value of cos pi/6 by:
 Using Trigonometric Functions
 Using Unit Circle
Cos pi/6 in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cos pi/6 as:
 ± √(1sin²(pi/6))
 ± 1/√(1 + tan²(pi/6))
 ± cot(pi/6)/√(1 + cot²(pi/6))
 ±√(cosec²(pi/6)  1)/cosec(pi/6)
 1/sec(pi/6)
Note: Since pi/6 lies in the 1st Quadrant, the final value of cos pi/6 will be positive.
We can use trigonometric identities to represent cos pi/6 as,
 cos(pi  pi/6) = cos 5pi/6
 cos(pi + pi/6) = cos 7pi/6
 sin(pi/2 + pi/6) = sin 2pi/3
 sin(pi/2  pi/6) = sin pi/3
Cos pi/6 Using Unit Circle
To find the value of cos π/6 using the unit circle:
 Rotate ‘r’ anticlockwise to form pi/6 angle with the positive xaxis.
 The cos of pi/6 equals the xcoordinate(0.866) of the point of intersection (0.866, 0.5) of unit circle and r.
Hence the value of cos pi/6 = x = 0.866 (approx)
☛ Also Check:
Examples Using Cos pi/6

Example 1: Find the value of (cos² pi/12  sin² pi/12). [Hint: Use cos pi/6 = 0.866]
Solution:
Using the cos 2a formula,
(cos² pi/12  sin² pi/12) = cos(2 × pi/12) = cos pi/6
∵ cos pi/6 = 0.866
⇒ (cos² pi/12  sin² pi/12) = 0.866 
Example 2: Find the value of 2 cos(pi/6)/3 sin(pi/3).
Solution:
Using trigonometric identities, we know, cos(pi/6) = sin(pi/2  pi/6) = sin pi/3.
⇒ cos(pi/6) = sin(pi/3)
⇒ Value of 2 cos(pi/6)/3 sin(pi/3) = 2/3 
Example 3: Simplify: 4 (cos(pi/6)/sin(2pi/3))
Solution:
We know cos pi/6 = sin 2pi/3
⇒ 4 cos(pi/6)/sin(2pi/3) = 4 (cos(pi/6)/cos(pi/6))
= 4(1) = 4
FAQs on Cos pi/6
What is Cos pi/6?
Cos pi/6 is the value of cosine trigonometric function for an angle equal to π/6 radians. The value of cos pi/6 is √3/2 or 0.866 (approx)
What is the Value of Cos pi/6 in Terms of Sin pi/6?
Using trigonometric identities, we can write cos pi/6 in terms of sin pi/6 as, cos(pi/6) = √(1  sin²(pi/6)). Here, the value of sin pi/6 is equal to 1/2.
How to Find Cos pi/6 in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cos pi/6 can be given in terms of other trigonometric functions as:
 ± √(1sin²(pi/6))
 ± 1/√(1 + tan²(pi/6))
 ± cot(pi/6)/√(1 + cot²(pi/6))
 ±√(cosec²(pi/6)  1)/cosec(pi/6)
 1/sec(pi/6)
☛ Also check: trigonometry table
What is the Exact Value of cos pi/6?
The exact value of cos pi/6 can be given accurately up to 8 decimal places as 0.86602540 and √3/2 in fraction.
How to Find the Value of Cos pi/6?
The value of cos pi/6 can be calculated by constructing an angle of π/6 radians with the xaxis, and then finding the coordinates of the corresponding point (0.866, 0.5) on the unit circle. The value of cos pi/6 is equal to the xcoordinate (0.866). ∴ cos pi/6 = 0.866.
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