Cot pi/6
The value of cot pi/6 is 1.7320508. . .. Cot pi/6 radians in degrees is written as cot ((π/6) × 180°/π), i.e., cot (30°). In this article, we will discuss the methods to find the value of cot pi/6 with examples.
 Cot pi/6: √3
 Cot pi/6 in decimal: 1.7320508. . .
 Cot (pi/6): 1.7320508. . . or √3
 Cot pi/6 in degrees: cot (30°)
What is the Value of Cot pi/6?
The value of cot pi/6 in decimal is 1.732050807. . .. Cot pi/6 can also be expressed using the equivalent of the given angle (pi/6) in degrees (30°).
We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)
⇒ pi/6 radians = pi/6 × (180°/pi) = 30° or 30 degrees
∴ cot pi/6 = cot π/6 = cot(30°) = √3 or 1.7320508. . .
Explanation:
For cot pi/6, the angle pi/6 lies between 0 and pi/2 (First Quadrant). Since cotangent function is positive in the first quadrant, thus cot pi/6 value = √3 or 1.7320508. . .
Since the cotangent function is a periodic function, we can represent cot pi/6 as, cot pi/6 = cot(pi/6 + n × pi), n ∈ Z.
⇒ cot pi/6 = cot 7pi/6 = cot 13pi/6 , and so on.
Note: Since, cotangent is an odd function, the value of cot(pi/6) = cot(pi/6).
Methods to Find Value of Cot pi/6
The cotangent function is positive in the 1st quadrant. The value of cot pi/6 is given as 1.73205. . .. We can find the value of cot pi/6 by:
 Using Unit Circle
 Using Trigonometric Functions
Cot pi/6 Using Unit Circle
To find the value of cot π/6 using the unit circle:
 Rotate ‘r’ anticlockwise to form pi/6 angle with the positive xaxis.
 The cot of pi/6 equals the xcoordinate(0.866) divided by ycoordinate(0.5) of the point of intersection (0.866, 0.5) of unit circle and r.
Hence the value of cot pi/6 = x/y = 1.7321 (approx)
Cot pi/6 in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cot pi/6 as:
 cos(pi/6)/sin(pi/6)
 ± cos(pi/6)/√(1  cos²(pi/6))
 ± √(1  sin²(pi/6))/sin(pi/6)
 ± 1/√(sec²(pi/6)  1)
 ± √(cosec²(pi/6)  1)
 1/tan(pi/6)
Note: Since pi/6 lies in the 1st Quadrant, the final value of cot pi/6 will be positive.
We can use trigonometric identities to represent cot pi/6 as,
 tan (pi/2  pi/6) = tan pi/3
 tan (pi/2 + pi/6) = tan 2pi/3
 cot (pi  pi/6) = cot 5pi/6
☛ Also Check:
Examples Using Cot pi/6

Example 1: Find the value of 6 cot(pi/6)/10 cot(5pi/6).
Solution:
Using trigonometric identities, we know, cot(pi/6) = cot(pi  pi/6) = cot 5pi/6.
⇒ cot(pi/6) = cot(5pi/6)
⇒ Value of 6 cot(pi/6)/10 cot(5pi/6) = 6/10 = 3/5 
Example 2: Using the value of cot pi/6, solve: (cosec²(pi/6)  1).
Solution:
We know, (cosec²(pi/6)  1) = (cot²(pi/6)) = 3
⇒ (cosec²(pi/6)  1) = 3 
Example 3: Simplify: 7 (cot(pi/6)/tan(pi/3))
Solution:
We know cot pi/6 = tan pi/3
⇒ 7 cot(pi/6)/tan(pi/3) = 7 (cot(pi/6)/cot(pi/6))
= 7(1) = 7
FAQs on Cot pi/6
What is Cot pi/6?
Cot pi/6 is the value of cotangent trigonometric function for an angle equal to π/6 radians. The value of cot pi/6 is √3 or 1.7321 (approx).
How to Find the Value of Cot pi/6?
The value of cot pi/6 can be calculated by constructing an angle of π/6 radians with the xaxis, and then finding the coordinates of the corresponding point (0.866, 0.5) on the unit circle. The value of cot pi/6 is equal to the xcoordinate(0.866) divided by the ycoordinate (0.5). ∴ cot pi/6 = 1.7321
How to Find Cot pi/6 in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cot pi/6 can be given in terms of other trigonometric functions as:
 cos(pi/6)/sin(pi/6)
 ± cos(pi/6)/√(1  cos²(pi/6))
 ± √(1  sin²(pi/6))/sin(pi/6)
 ± 1/√(sec²(pi/6)  1)
 ± √(cosec²(pi/6)  1)
 1/tan(pi/6)
☛ Also check: trigonometry table
What is the Exact Value of Cot pi/6?
The exact value of cot pi/6 can be given accurately up to 8 decimal places as 1.73205080 or as √3.
What is the Value of Cot pi/6 in Terms of Sin pi/6?
Using trigonometric identities, we can write cot pi/6 in terms of sin pi/6 as, cot(pi/6) = √(1  sin²(pi/6))/sin pi/6 . Here, the value of sin pi/6 is equal to 1/2.
visual curriculum