Cot 60 Degrees
The value of cot 60 degrees is 0.5773502. . .. Cot 60 degrees in radians is written as cot (60° × π/180°), i.e., cot (π/3) or cot (1.047197. . .). In this article, we will discuss the methods to find the value of cot 60 degrees with examples.
 Cot 60°: 1/√3
 Cot 60° in decimal: 0.5773502. . .
 Cot (60 degrees): 0.5773502. . . or (1/√3)
 Cot 60° in radians: cot (π/3) or cot (1.0471975 . . .)
What is the Value of Cot 60 Degrees?
The value of cot 60 degrees in decimal is 0.577350269. . .. Cot 60 degrees can also be expressed using the equivalent of the given angle (60 degrees) in radians (1.04719 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 60 degrees = 60° × (π/180°) rad = π/3 or 1.0471 . . .
∴ cot 60° = cot(1.0471) = 1/√3 or 0.5773502. . .
Explanation:
For cot 60 degrees, the angle 60° lies between 0° and 90° (First Quadrant). Since cotangent function is positive in the first quadrant, thus cot 60° value = 1/√3 or 0.5773502. . .
Since the cotangent function is a periodic function, we can represent cot 60° as, cot 60 degrees = cot(60° + n × 180°), n ∈ Z.
⇒ cot 60° = cot 240° = cot 420°, and so on.
Note: Since, cotangent is an odd function, the value of cot(60°) = cot(60°).
Methods to Find Value of Cot 60 Degrees
The cotangent function is positive in the 1st quadrant. The value of cot 60° is given as 0.57735. . . We can find the value of cot 60 degrees by:
 Using Trigonometric Functions
 Using Unit Circle
Cot 60° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cot 60 degrees as:
 cos(60°)/sin(60°)
 ± cos 60°/√(1  cos²(60°))
 ± √(1  sin²(60°))/sin 60°
 ± 1/√(sec²(60°)  1)
 ± √(cosec²(60°)  1)
 1/tan 60°
Note: Since 60° lies in the 1st Quadrant, the final value of cot 60° will be positive.
We can use trigonometric identities to represent cot 60° as,
 tan (90°  60°) = tan 30°
 tan (90° + 60°) = tan 150°
 cot (180°  60°) = cot 120°
Cot 60 Degrees Using Unit Circle
To find the value of cot 60 degrees using the unit circle:
 Rotate ‘r’ anticlockwise to form 60° angle with the positive xaxis.
 The cot of 60 degrees 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 60° = x/y = 0.5774 (approx).
☛ Also Check:
Examples Using Cot 60 Degrees

Example 1: Find the value of 2 cot(60°)/9 cot(120°).
Solution:
Using trigonometric identities, we know, cot(60°) = cot(180°  60°) = cot 120°.
⇒ cot(60°) = cot(120°)
⇒ Value of 2 cot(60°)/9 cot(120°) = 2/9 
Example 2: Simplify: 4 (cot 60°/tan 30°)
Solution:
We know cot 60° = tan 30°
⇒ 4 cot 60°/tan 30° = 4 (cot 60°/cot 60°)
= 4(1) = 4 
Example 3: Find the value of cot 60° if tan 60° is 1.7320.
Solution:
Since, cot 60° = 1/tan 60°
⇒ cot 60° = 1/1.7320 = 0.5774
FAQs on Cot 60 Degrees
What is Cot 60 Degrees?
Cot 60 degrees is the value of cotangent trigonometric function for an angle equal to 60 degrees. The value of cot 60° is 1/√3 or 0.5774 (approx).
How to Find Cot 60° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cot 60° can be given in terms of other trigonometric functions as:
 cos(60°)/sin(60°)
 ± cos 60°/√(1  cos²(60°))
 ± √(1  sin²(60°))/sin 60°
 ± 1/√(sec²(60°)  1)
 ± √(cosec²(60°)  1)
 1/tan 60°
☛ Also check: trigonometric table
What is the Value of Cot 60° in Terms of Cosec 60°?
Since the cotangent function can be represented using the cosecant function, we can write cot 60° as √(cosec²(60°)  1). The value of cosec 60° is equal to 1.15470.
How to Find the Value of Cot 60 Degrees?
The value of cot 60 degrees can be calculated by constructing an angle of 60° with the xaxis, and then finding the coordinates of the corresponding point (0.5, 0.866) on the unit circle. The value of cot 60° is equal to the xcoordinate(0.5) divided by the ycoordinate (0.866). ∴ cot 60° = 0.5774
What is the Value of Cot 60 Degrees in Terms of Tan 60°?
Since the cotangent function is the reciprocal of the tangent function, we can write cot 60° as 1/tan(60°). The value of tan 60° is equal to √3.
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