Cot 2pi/3
The value of cot 2pi/3 is 0.5773502. . .. Cot 2pi/3 radians in degrees is written as cot ((2π/3) × 180°/π), i.e., cot (120°). In this article, we will discuss the methods to find the value of cot 2pi/3 with examples.
 Cot 2pi/3: (1/√3)
 Cot 2pi/3 in decimal: 0.5773502. . .
 Cot (2pi/3): 0.5773502. . . or 1/√3
 Cot 2pi/3 in degrees: cot (120°)
What is the Value of Cot 2pi/3?
The value of cot 2pi/3 in decimal is 0.577350269. . .. Cot 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
∴ cot 2pi/3 = cot 2π/3 = cot(120°) = (1/√3) or 0.5773502. . .
Explanation:
For cot 2pi/3, the angle 2pi/3 lies between pi/2 and pi (Second Quadrant). Since cotangent function is negative in the second quadrant, thus cot 2pi/3 value = (1/√3) or 0.5773502. . .
Since the cotangent function is a periodic function, we can represent cot 2pi/3 as, cot 2pi/3 = cot(2pi/3 + n × pi), n ∈ Z.
⇒ cot 2pi/3 = cot 5pi/3 = cot 8pi/3 , and so on.
Note: Since, cotangent is an odd function, the value of cot(2pi/3) = cot(2pi/3).
Methods to Find Value of Cot 2pi/3
The cotangent function is negative in the 2nd quadrant. The value of cot 2pi/3 is given as 0.57735. . .. We can find the value of cot 2pi/3 by:
 Using Unit Circle
 Using Trigonometric Functions
Cot 2pi/3 Using Unit Circle
To find the value of cot 2π/3 using the unit circle:
 Rotate ‘r’ anticlockwise to form 2pi/3 angle with the positive xaxis.
 The cot of 2pi/3 equals the xcoordinate(0.5) divided by ycoordinate(0.866) of the point of intersection (0.5, 0.866) of unit circle and r.
Hence the value of cot 2pi/3 = x/y = 0.5774 (approx)
Cot 2pi/3 in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cot 2pi/3 as:
 cos(2pi/3)/sin(2pi/3)
 ± cos(2pi/3)/√(1  cos²(2pi/3))
 ± √(1  sin²(2pi/3))/sin(2pi/3)
 ± 1/√(sec²(2pi/3)  1)
 ± √(cosec²(2pi/3)  1)
 1/tan(2pi/3)
Note: Since 2pi/3 lies in the 2nd Quadrant, the final value of cot 2pi/3 will be negative.
We can use trigonometric identities to represent cot 2pi/3 as,
 tan (pi/2  2pi/3) = tan(pi/6)
 tan (pi/2 + 2pi/3) = tan 7pi/6
 cot (pi  2pi/3) = cot pi/3
☛ Also Check:
Examples Using Cot 2pi/3

Example 1: Find the value of cot 2pi/3 if tan 2pi/3 is 1.7320.
Solution:
Since, cot 2pi/3 = 1/tan(2pi/3)
⇒ cot 2pi/3 = 1/(1.7320) = 0.5774 
Example 2: Find the value of (cos (2pi/3) cosec (pi/3) sec (pi/3))/2. [Hint: Use cot 2pi/3 = 0.5774]
Solution:
Using trigonometry formulas,
(cos (2pi/3) cosec (pi/3) sec (pi/3))/2 = cos (2pi/3)/(2 sin (pi/3) cos (pi/3))
Using sin 2a formula,
2 sin (pi/3) cos (pi/3) = sin (2 × pi/3) = sin 2pi/3
⇒ cos (2pi/3) / sin (2pi/3) = cot 2pi/3
⇒ (cos (2pi/3) cosec (pi/3) sec (pi/3))/2 = 0.5774 
Example 3: Simplify: 5 (cot(2pi/3)/tan(pi/6))
Solution:
We know cot 2pi/3 = tan(pi/6)
⇒ 5 cot(2pi/3)/tan(pi/6) = 5 (cot(2pi/3)/cot(2pi/3))
= 5(1) = 5
FAQs on Cot 2pi/3
What is Cot 2pi/3?
Cot 2pi/3 is the value of cotangent trigonometric function for an angle equal to 2π/3 radians. The value of cot 2pi/3 is (1/√3) or 0.5774 (approx).
How to Find Cot 2pi/3 in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cot 2pi/3 can be given in terms of other trigonometric functions as:
 cos(2pi/3)/sin(2pi/3)
 ± cos(2pi/3)/√(1  cos²(2pi/3))
 ± √(1  sin²(2pi/3))/sin(2pi/3)
 ± 1/√(sec²(2pi/3)  1)
 ± √(cosec²(2pi/3)  1)
 1/tan(2pi/3)
☛ Also check: trigonometric table
How to Find the Value of Cot 2pi/3?
The value of cot 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 cot 2pi/3 is equal to the xcoordinate(0.5) divided by the ycoordinate (0.866). ∴ cot 2pi/3 = 0.5774
What is the Value of Cot 2pi/3 in Terms of Tan 2pi/3?
Since the cotangent function is the reciprocal of the tangent function, we can write cot 2pi/3 as 1/tan(2pi/3). The value of tan 2pi/3 is equal to √3.
What is the Value of Cot 2pi/3 in Terms of Sec 2pi/3?
We can represent the cotangent function in terms of the secant function using trig identities, cot 2pi/3 can be written as 1/√(sec²(2pi/3)  1). Here, the value of sec 2pi/3 is equal to 2.
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