Cot 4pi/3
The value of cot 4pi/3 is 0.5773502. . .. Cot 4pi/3 radians in degrees is written as cot ((4π/3) × 180°/π), i.e., cot (240°). In this article, we will discuss the methods to find the value of cot 4pi/3 with examples.
 Cot 4pi/3: 1/√3
 Cot 4pi/3 in decimal: 0.5773502. . .
 Cot (4pi/3): 0.5773502. . . or (1/√3)
 Cot 4pi/3 in degrees: cot (240°)
What is the Value of Cot 4pi/3?
The value of cot 4pi/3 in decimal is 0.577350269. . .. Cot 4pi/3 can also be expressed using the equivalent of the given angle (4pi/3) in degrees (240°).
We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)
⇒ 4pi/3 radians = 4pi/3 × (180°/pi) = 240° or 240 degrees
∴ cot 4pi/3 = cot 4π/3 = cot(240°) = 1/√3 or 0.5773502. . .
Explanation:
For cot 4pi/3, the angle 4pi/3 lies between pi and 3pi/2 (Third Quadrant). Since cotangent function is positive in the third quadrant, thus cot 4pi/3 value = 1/√3 or 0.5773502. . .
Since the cotangent function is a periodic function, we can represent cot 4pi/3 as, cot 4pi/3 = cot(4pi/3 + n × pi), n ∈ Z.
⇒ cot 4pi/3 = cot 7pi/3 = cot 10pi/3 , and so on.
Note: Since, cotangent is an odd function, the value of cot(4pi/3) = cot(4pi/3).
Methods to Find Value of Cot 4pi/3
The cotangent function is positive in the 3rd quadrant. The value of cot 4pi/3 is given as 0.57735. . .. We can find the value of cot 4pi/3 by:
 Using Trigonometric Functions
 Using Unit Circle
Cot 4pi/3 in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cot 4pi/3 as:
 cos(4pi/3)/sin(4pi/3)
 ± cos(4pi/3)/√(1  cos²(4pi/3))
 ± √(1  sin²(4pi/3))/sin(4pi/3)
 ± 1/√(sec²(4pi/3)  1)
 ± √(cosec²(4pi/3)  1)
 1/tan(4pi/3)
Note: Since 4pi/3 lies in the 3rd Quadrant, the final value of cot 4pi/3 will be positive.
We can use trigonometric identities to represent cot 4pi/3 as,
 tan (pi/2  4pi/3) = tan(5pi/6)
 tan (pi/2 + 4pi/3) = tan 11pi/6
 cot (pi  4pi/3) = cot(pi/3)
Cot 4pi/3 Using Unit Circle
To find the value of cot 4π/3 using the unit circle:
 Rotate ‘r’ anticlockwise to form 4pi/3 angle with the positive xaxis.
 The cot of 4pi/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 4pi/3 = x/y = 0.5774 (approx)
☛ Also Check:
Examples Using Cot 4pi/3

Example 1: Simplify: 9 (cot(4pi/3)/tan(5pi/6))
Solution:
We know cot 4pi/3 = tan(5pi/6)
⇒ 9 cot(4pi/3)/tan(5pi/6) = 9 (cot(4pi/3)/cot(4pi/3))
= 9(1) = 9 
Example 2: Find the value of cot 4pi/3 if tan 4pi/3 is 1.7320.
Solution:
Since, cot 4pi/3 = 1/tan(4pi/3)
⇒ cot 4pi/3 = 1/1.7320 = 0.5774 
Example 3: Find the value of 6 cot(4pi/3)/10 cot(pi/3).
Solution:
Using trigonometric identities, we know, cot(4pi/3) = cot(pi  4pi/3) = cot(pi/3).
⇒ cot(4pi/3) = cot(pi/3)
⇒ Value of 6 cot(4pi/3)/10 cot(pi/3) = 6/10 = 3/5
FAQs on Cot 4pi/3
What is Cot 4pi/3?
Cot 4pi/3 is the value of cotangent trigonometric function for an angle equal to 4π/3 radians. The value of cot 4pi/3 is 1/√3 or 0.5774 (approx).
How to Find the Value of Cot 4pi/3?
The value of cot 4pi/3 can be calculated by constructing an angle of 4π/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 4pi/3 is equal to the xcoordinate(0.5) divided by the ycoordinate (0.866). ∴ cot 4pi/3 = 0.5774
What is the Value of Cot 4pi/3 in Terms of Cosec 4pi/3?
Since the cotangent function can be represented using the cosecant function, we can write cot 4pi/3 as √(cosec²(4pi/3)  1). The value of cosec 4pi/3 is equal to 1.15470.
What is the Value of Cot 4pi/3 in Terms of Sin 4pi/3?
Using trigonometric identities, we can write cot 4pi/3 in terms of sin 4pi/3 as, cot(4pi/3) = √(1  sin²(4pi/3))/sin 4pi/3 . Here, the value of sin 4pi/3 is equal to (√3/2).
How to Find Cot 4pi/3 in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cot 4pi/3 can be given in terms of other trigonometric functions as:
 cos(4pi/3)/sin(4pi/3)
 ± cos(4pi/3)/√(1  cos²(4pi/3))
 ± √(1  sin²(4pi/3))/sin(4pi/3)
 ± 1/√(sec²(4pi/3)  1)
 ± √(cosec²(4pi/3)  1)
 1/tan(4pi/3)
☛ Also check: trigonometric table
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