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Cot 5pi/6
The value of cot 5pi/6 is 1.7320508. . .. Cot 5pi/6 radians in degrees is written as cot ((5π/6) × 180°/π), i.e., cot (150°). In this article, we will discuss the methods to find the value of cot 5pi/6 with examples.
 Cot 5pi/6: √3
 Cot 5pi/6 in decimal: 1.7320508. . .
 Cot (5pi/6): 1.7320508. . . or √3
 Cot 5pi/6 in degrees: cot (150°)
What is the Value of Cot 5pi/6?
The value of cot 5pi/6 in decimal is 1.732050807. . .. Cot 5pi/6 can also be expressed using the equivalent of the given angle (5pi/6) in degrees (150°).
We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)
⇒ 5pi/6 radians = 5pi/6 × (180°/pi) = 150° or 150 degrees
∴ cot 5pi/6 = cot 5π/6 = cot(150°) = √3 or 1.7320508. . .
Explanation:
For cot 5pi/6, the angle 5pi/6 lies between pi/2 and pi (Second Quadrant). Since cotangent function is negative in the second quadrant, thus cot 5pi/6 value = √3 or 1.7320508. . .
Since the cotangent function is a periodic function, we can represent cot 5pi/6 as, cot 5pi/6 = cot(5pi/6 + n × pi), n ∈ Z.
⇒ cot 5pi/6 = cot 11pi/6 = cot 17pi/6 , and so on.
Note: Since, cotangent is an odd function, the value of cot(5pi/6) = cot(5pi/6).
Methods to Find Value of Cot 5pi/6
The cotangent function is negative in the 2nd quadrant. The value of cot 5pi/6 is given as 1.73205. . .. We can find the value of cot 5pi/6 by:
 Using Trigonometric Functions
 Using Unit Circle
Cot 5pi/6 in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cot 5pi/6 as:
 cos(5pi/6)/sin(5pi/6)
 ± cos(5pi/6)/√(1  cos²(5pi/6))
 ± √(1  sin²(5pi/6))/sin(5pi/6)
 ± 1/√(sec²(5pi/6)  1)
 ± √(cosec²(5pi/6)  1)
 1/tan(5pi/6)
Note: Since 5pi/6 lies in the 2nd Quadrant, the final value of cot 5pi/6 will be negative.
We can use trigonometric identities to represent cot 5pi/6 as,
 tan (pi/2  5pi/6) = tan(pi/3)
 tan (pi/2 + 5pi/6) = tan 4pi/3
 cot (pi  5pi/6) = cot pi/6
Cot 5pi/6 Using Unit Circle
To find the value of cot 5π/6 using the unit circle:
 Rotate ‘r’ anticlockwise to form 5pi/6 angle with the positive xaxis.
 The cot of 5pi/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 5pi/6 = x/y = 1.7321 (approx)
☛ Also Check:
Examples Using Cot 5pi/6

Example 1: Using the value of cot 5pi/6, solve: (cosec²(5pi/6)  1).
Solution:
We know, (cosec²(5pi/6)  1) = (cot²(5pi/6)) = 3
⇒ (cosec²(5pi/6)  1) = 3 
Example 2: Find the value of (cos (5pi/6) cosec (5pi/12) sec (5pi/12))/2. [Hint: Use cot 5pi/6 = 1.7321]
Solution:
Using trigonometry formulas,
(cos (5pi/6) cosec (5pi/12) sec (5pi/12))/2 = cos (5pi/6)/(2 sin (5pi/12) cos (5pi/12))
Using sin 2a formula,
2 sin (5pi/12) cos (5pi/12) = sin (2 × 5pi/12) = sin 5pi/6
⇒ cos (5pi/6) / sin (5pi/6) = cot 5pi/6
⇒ (cos (5pi/6) cosec (5pi/12) sec (5pi/12))/2 = 1.7321 
Example 3: Find the value of 5 cot(5pi/6)/6 cot(pi/6).
Solution:
Using trigonometric identities, we know, cot(5pi/6) = cot(pi  5pi/6) = cot pi/6.
⇒ cot(5pi/6) = cot(pi/6)
⇒ Value of 5 cot(5pi/6)/6 cot(pi/6) = 5/6
FAQs on Cot 5pi/6
What is Cot 5pi/6?
Cot 5pi/6 is the value of cotangent trigonometric function for an angle equal to 5π/6 radians. The value of cot 5pi/6 is √3 or 1.7321 (approx).
How to Find Cot 5pi/6 in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cot 5pi/6 can be given in terms of other trigonometric functions as:
 cos(5pi/6)/sin(5pi/6)
 ± cos(5pi/6)/√(1  cos²(5pi/6))
 ± √(1  sin²(5pi/6))/sin(5pi/6)
 ± 1/√(sec²(5pi/6)  1)
 ± √(cosec²(5pi/6)  1)
 1/tan(5pi/6)
☛ Also check: trigonometric table
What is the Value of Cot 5pi/6 in Terms of Cosec 5pi/6?
Since the cotangent function can be represented using the cosecant function, we can write cot 5pi/6 as √(cosec²(5pi/6)  1). The value of cosec 5pi/6 is equal to 2.
How to Find the Value of Cot 5pi/6?
The value of cot 5pi/6 can be calculated by constructing an angle of 5π/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 5pi/6 is equal to the xcoordinate(0.866) divided by the ycoordinate (0.5). ∴ cot 5pi/6 = 1.7321
What is the Value of Cot 5pi/6 in Terms of Cos 5pi/6?
We know, using trig identities, we can write cot 5pi/6 as cos(5pi/6)/√(1  cos²(5pi/6)). Here, the value of cos 5pi/6 is equal to 0.866025.
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