Cos 2pi/7
The value of cos 2pi/7 is 0.6234898. . .. Cos 2pi/7 radians in degrees is written as cos ((2π/7) × 180°/π), i.e., cos (51.4285714°). In this article, we will discuss the methods to find the value of cos 2pi/7 with examples.
 Cos 2pi/7 in decimal: 0.6234898. . .
 Cos (2pi/7): 0.6234898. . .
 Cos 2pi/7 in degrees: cos (51.4285714°)
What is the Value of Cos 2pi/7?
The value of cos 2pi/7 in decimal is 0.623489802. . .. Cos 2pi/7 can also be expressed using the equivalent of the given angle (2pi/7) in degrees (51.4285714°).
We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)
⇒ 2pi/7 radians = 2pi/7 × (180°/pi) = 51.4285714° or 51.4285714 degrees
∴ cos 2pi/7 = cos 2π/7 = cos(51.4285714°) = 0.6234898. . .
Explanation:
For cos 2pi/7, the angle 2pi/7 lies between 0 and pi/2 (First Quadrant). Since cosine function is positive in the first quadrant, thus cos 2pi/7 value = 0.6234898. . .
Since the cosine function is a periodic function, we can represent cos 2pi/7 as, cos 2pi/7 = cos(2pi/7 + n × 2pi), n ∈ Z.
⇒ cos 2pi/7 = cos 16pi/7 = cos 30pi/7 , and so on.
Note: Since, cosine is an even function, the value of cos(2pi/7) = cos(2pi/7).
Methods to Find Value of Cos 2pi/7
The cosine function is positive in the 1st quadrant. The value of cos 2pi/7 is given as 0.62348. . .. We can find the value of cos 2pi/7 by:
 Using Trigonometric Functions
 Using Unit Circle
Cos 2pi/7 in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cos 2pi/7 as:
 ± √(1sin²(2pi/7))
 ± 1/√(1 + tan²(2pi/7))
 ± cot(2pi/7)/√(1 + cot²(2pi/7))
 ±√(cosec²(2pi/7)  1)/cosec(2pi/7)
 1/sec(2pi/7)
Note: Since 2pi/7 lies in the 1st Quadrant, the final value of cos 2pi/7 will be positive.
We can use trigonometric identities to represent cos 2pi/7 as,
 cos(pi  2pi/7) = cos 5pi/7
 cos(pi + 2pi/7) = cos 9pi/7
 sin(pi/2 + 2pi/7) = sin 11pi/14
 sin(pi/2  2pi/7) = sin 3pi/14
Cos 2pi/7 Using Unit Circle
To find the value of cos 2π/7 using the unit circle:
 Rotate ‘r’ anticlockwise to form 2pi/7 angle with the positive xaxis.
 The cos of 2pi/7 equals the xcoordinate(0.6235) of the point of intersection (0.6235, 0.7818) of unit circle and r.
Hence the value of cos 2pi/7 = x = 0.6235 (approx)
☛ Also Check:
Examples Using Cos 2pi/7

Example 1: Using the value of cos 2pi/7, solve: (1sin²(2pi/7)).
Solution:
We know, (1sin²(2pi/7)) = (cos²(2pi/7)) = 0.3887
⇒ (1sin²(2pi/7)) = 0.3887 
Example 2: Find the value of cos 2pi/7 if sec 2pi/7 is 1.6038.
Solution:
Since, cos 2pi/7 = 1/sec(2pi/7)
⇒ cos 2pi/7 = 1/1.6038 = 0.6235 
Example 3: Simplify: 5 (cos(2pi/7)/sin(11pi/14))
Solution:
We know cos 2pi/7 = sin 11pi/14
⇒ 5 cos(2pi/7)/sin(11pi/14) = 5 (cos(2pi/7)/cos(2pi/7))
= 5(1) = 5
FAQs on Cos 2pi/7
What is Cos 2pi/7?
Cos 2pi/7 is the value of cosine trigonometric function for an angle equal to 2π/7 radians. The value of cos 2pi/7 is 0.6235 (approx).
What is the Value of Cos 2pi/7 in Terms of Cosec 2pi/7?
Since the cosine function can be represented using the cosecant function, we can write cos 2pi/7 as [√(cosec²(2pi/7)  1)/cosec 2pi/7]. The value of cosec 2pi/7 is equal to 1.27904.
How to Find Cos 2pi/7 in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cos 2pi/7 can be given in terms of other trigonometric functions as:
 ± √(1sin²(2pi/7))
 ± 1/√(1 + tan²(2pi/7))
 ± cot(2pi/7)/√(1 + cot²(2pi/7))
 ±√(cosec²(2pi/7)  1)/cosec(2pi/7)
 1/sec(2pi/7)
☛ Also check: trigonometric table
How to Find the Value of Cos 2pi/7?
The value of cos 2pi/7 can be calculated by constructing an angle of 2π/7 radians with the xaxis, and then finding the coordinates of the corresponding point (0.6235, 0.7818) on the unit circle. The value of cos 2pi/7 is equal to the xcoordinate (0.6235). ∴ cos 2pi/7 = 0.6235.
What is the Value of Cos 2pi/7 in Terms of Sin 2pi/7?
Using trigonometric identities, we can write cos 2pi/7 in terms of sin 2pi/7 as, cos(2pi/7) = √(1  sin²(2pi/7)). Here, the value of sin 2pi/7 is equal to 0.7818.
visual curriculum