Cot pi/3
The value of cot pi/3 is 0.5773502. . .. Cot pi/3 radians in degrees is written as cot ((π/3) × 180°/π), i.e., cot (60°). In this article, we will discuss the methods to find the value of cot pi/3 with examples.
 Cot pi/3: 1/√3
 Cot pi/3 in decimal: 0.5773502. . .
 Cot (pi/3): 0.5773502. . . or (1/√3)
 Cot pi/3 in degrees: cot (60°)
What is the Value of Cot pi/3?
The value of cot pi/3 in decimal is 0.577350269. . .. Cot pi/3 can also be expressed using the equivalent of the given angle (pi/3) in degrees (60°).
We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)
⇒ pi/3 radians = pi/3 × (180°/pi) = 60° or 60 degrees
∴ cot pi/3 = cot π/3 = cot(60°) = 1/√3 or 0.5773502. . .
Explanation:
For cot pi/3, the angle pi/3 lies between 0 and pi/2 (First Quadrant). Since cotangent function is positive in the first quadrant, thus cot pi/3 value = 1/√3 or 0.5773502. . .
Since the cotangent function is a periodic function, we can represent cot pi/3 as, cot pi/3 = cot(pi/3 + n × pi), n ∈ Z.
⇒ cot pi/3 = cot 4pi/3 = cot 7pi/3 , and so on.
Note: Since, cotangent is an odd function, the value of cot(pi/3) = cot(pi/3).
Methods to Find Value of Cot pi/3
The cotangent function is positive in the 1st quadrant. The value of cot pi/3 is given as 0.57735. . .. We can find the value of cot pi/3 by:
 Using Trigonometric Functions
 Using Unit Circle
Cot pi/3 in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cot pi/3 as:
 cos(pi/3)/sin(pi/3)
 ± cos(pi/3)/√(1  cos²(pi/3))
 ± √(1  sin²(pi/3))/sin(pi/3)
 ± 1/√(sec²(pi/3)  1)
 ± √(cosec²(pi/3)  1)
 1/tan(pi/3)
Note: Since pi/3 lies in the 1st Quadrant, the final value of cot pi/3 will be positive.
We can use trigonometric identities to represent cot pi/3 as,
 tan (pi/2  pi/3) = tan pi/6
 tan (pi/2 + pi/3) = tan 5pi/6
 cot (pi  pi/3) = cot 2pi/3
Cot pi/3 Using Unit Circle
To find the value of cot π/3 using the unit circle:
 Rotate ‘r’ anticlockwise to form pi/3 angle with the positive xaxis.
 The cot of pi/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 pi/3 = x/y = 0.5774 (approx)
☛ Also Check:
Examples Using Cot pi/3

Example 1: Using the value of cot pi/3, solve: (cosec²(pi/3)  1).
Solution:
We know, (cosec²(pi/3)  1) = (cot²(pi/3)) = 0.3333
⇒ (cosec²(pi/3)  1) = 0.3333 
Example 2: Simplify: 9 (cot(pi/3)/tan(pi/6))
Solution:
We know cot pi/3 = tan pi/6
⇒ 9 cot(pi/3)/tan(pi/6) = 9 (cot(pi/3)/cot(pi/3))
= 9(1) = 9 
Example 3: Find the value of (cos (pi/3) cosec (pi/6) sec (pi/6))/2. [Hint: Use cot pi/3 = 0.5774]
Solution:
Using trigonometry formulas,
(cos (pi/3) cosec (pi/6) sec (pi/6))/2 = cos (pi/3)/(2 sin (pi/6) cos (pi/6))
Using sin 2a formula,
2 sin (pi/6) cos (pi/6) = sin (2 × pi/6) = sin pi/3
⇒ cos (pi/3) / sin (pi/3) = cot pi/3
⇒ (cos (pi/3) cosec (pi/6) sec (pi/6))/2 = 0.5774
FAQs on Cot pi/3
What is Cot pi/3?
Cot pi/3 is the value of cotangent trigonometric function for an angle equal to π/3 radians. The value of cot pi/3 is 1/√3 or 0.5774 (approx).
How to Find the Value of Cot pi/3?
The value of cot pi/3 can be calculated by constructing an angle of π/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 pi/3 is equal to the xcoordinate(0.5) divided by the ycoordinate (0.866). ∴ cot pi/3 = 0.5774
How to Find Cot pi/3 in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cot pi/3 can be given in terms of other trigonometric functions as:
 cos(pi/3)/sin(pi/3)
 ± cos(pi/3)/√(1  cos²(pi/3))
 ± √(1  sin²(pi/3))/sin(pi/3)
 ± 1/√(sec²(pi/3)  1)
 ± √(cosec²(pi/3)  1)
 1/tan(pi/3)
☛ Also check: trigonometry table
What is the Value of Cot pi/3 in Terms of Sin pi/3?
Using trigonometric identities, we can write cot pi/3 in terms of sin pi/3 as, cot(pi/3) = √(1  sin²(pi/3))/sin pi/3 . Here, the value of sin pi/3 is equal to √3/2.
What is the Value of Cot pi/3 in Terms of Cosec pi/3?
Since the cotangent function can be represented using the cosecant function, we can write cot pi/3 as √(cosec²(pi/3)  1). The value of cosec pi/3 is equal to 1.15470.
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