Cos 2pi/3
The value of cos 2pi/3 is 0.5. Cos 2pi/3 radians in degrees is written as cos ((2π/3) × 180°/π), i.e., cos (120°). In this article, we will discuss the methods to find the value of cos 2pi/3 with examples.
 Cos 2pi/3: (1/2)
 Cos 2pi/3 in decimal: 0.5
 Cos (2pi/3): 0.5 or (1/2)
 Cos 2pi/3 in degrees: cos (120°)
What is the Value of Cos 2pi/3?
The value of cos 2pi/3 in decimal is 0.5. Cos 2pi/3 can also be expressed using the equivalent of the given angle (2pi/3) in degrees (120°).
We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)
⇒ 2pi/3 radians = 2pi/3 × (180°/pi) = 120° or 120 degrees
∴ cos 2pi/3 = cos 2π/3 = cos(120°) = (1/2) or 0.5
Explanation:
For cos 2pi/3, the angle 2pi/3 lies between pi/2 and pi (Second Quadrant). Since cosine function is negative in the second quadrant, thus cos 2pi/3 value = (1/2) or 0.5
Since the cosine function is a periodic function, we can represent cos 2pi/3 as, cos 2pi/3 = cos(2pi/3 + n × 2pi), n ∈ Z.
⇒ cos 2pi/3 = cos 8pi/3 = cos 14pi/3 , and so on.
Note: Since, cosine is an even function, the value of cos(2pi/3) = cos(2pi/3).
Methods to Find Value of Cos 2pi/3
The cosine function is negative in the 2nd quadrant. The value of cos 2pi/3 is given as 0.5. We can find the value of cos 2pi/3 by:
 Using Unit Circle
 Using Trigonometric Functions
Cos 2pi/3 Using Unit Circle
To find the value of cos 2π/3 using the unit circle:
 Rotate ‘r’ anticlockwise to form 2pi/3 angle with the positive xaxis.
 The cos of 2pi/3 equals the xcoordinate(0.5) of the point of intersection (0.5, 0.866) of unit circle and r.
Hence the value of cos 2pi/3 = x = 0.5
Cos 2pi/3 in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cos 2pi/3 as:
 ± √(1sin²(2pi/3))
 ± 1/√(1 + tan²(2pi/3))
 ± cot(2pi/3)/√(1 + cot²(2pi/3))
 ±√(cosec²(2pi/3)  1)/cosec(2pi/3)
 1/sec(2pi/3)
Note: Since 2pi/3 lies in the 2nd Quadrant, the final value of cos 2pi/3 will be negative.
We can use trigonometric identities to represent cos 2pi/3 as,
 cos(pi  2pi/3) = cos pi/3
 cos(pi + 2pi/3) = cos 5pi/3
 sin(pi/2 + 2pi/3) = sin 7pi/6
 sin(pi/2  2pi/3) = sin(pi/6)
☛ Also Check:
Examples Using Cos 2pi/3

Example 1: Find the value of cos 2pi/3 if sec 2pi/3 is 2.
Solution:
Since, cos 2pi/3 = 1/sec(2pi/3)
⇒ cos 2pi/3 = 1/(2) = 0.5 
Example 2: Using the value of cos 2pi/3, solve: (1sin²(2pi/3)).
Solution:
We know, (1sin²(2pi/3)) = (cos²(2pi/3)) = 0.25
⇒ (1sin²(2pi/3)) = 0.25 
Example 3: Find the value of 2 cos(2pi/3)/3 sin(pi/6).
Solution:
Using trigonometric identities, we know, cos(2pi/3) = sin(pi/2  2pi/3) = sin(pi/6).
⇒ cos(2pi/3) = sin(pi/6)
⇒ Value of 2 cos(2pi/3)/3 sin(pi/6) = 2/3
FAQs on Cos 2pi/3
What is Cos 2pi/3?
Cos 2pi/3 is the value of cosine trigonometric function for an angle equal to 2π/3 radians. The value of cos 2pi/3 is (1/2) or 0.5
What is the Exact Value of cos 2pi/3?
The exact value of cos 2pi/3 is 0.5.
What is the Value of Cos 2pi/3 in Terms of Tan 2pi/3?
We know, using trig identities, we can write cos 2pi/3 as 1/√(1 + tan²(2pi/3)). Here, the value of tan 2pi/3 is equal to 1.732050.
How to Find the Value of Cos 2pi/3?
The value of cos 2pi/3 can be calculated by constructing an angle of 2π/3 radians with the xaxis, and then finding the coordinates of the corresponding point (0.5, 0.866) on the unit circle. The value of cos 2pi/3 is equal to the xcoordinate (0.5). ∴ cos 2pi/3 = 0.5.
How to Find Cos 2pi/3 in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cos 2pi/3 can be given in terms of other trigonometric functions as:
 ± √(1sin²(2pi/3))
 ± 1/√(1 + tan²(2pi/3))
 ± cot(2pi/3)/√(1 + cot²(2pi/3))
 ±√(cosec²(2pi/3)  1)/cosec(2pi/3)
 1/sec(2pi/3)
☛ Also check: trigonometry table
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