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Cot 30 Degrees
The value of cot 30 degrees is 1.7320508. . .. Cot 30 degrees in radians is written as cot (30° × π/180°), i.e., cot (π/6) or cot (0.523598. . .). In this article, we will discuss the methods to find the value of cot 30 degrees with examples.
 Cot 30°: √3
 Cot 30° in decimal: 1.7320508. . .
 Cot (30 degrees): 1.7320508. . . or √3
 Cot 30° in radians: cot (π/6) or cot (0.5235987 . . .)
What is the Value of Cot 30 Degrees?
The value of cot 30 degrees in decimal is 1.732050807. . .. Cot 30 degrees can also be expressed using the equivalent of the given angle (30 degrees) in radians (0.52359 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 30 degrees = 30° × (π/180°) rad = π/6 or 0.5235 . . .
∴ cot 30° = cot(0.5235) = √3 or 1.7320508. . .
Explanation:
For cot 30 degrees, the angle 30° lies between 0° and 90° (First Quadrant). Since cotangent function is positive in the first quadrant, thus cot 30° value = √3 or 1.7320508. . .
Since the cotangent function is a periodic function, we can represent cot 30° as, cot 30 degrees = cot(30° + n × 180°), n ∈ Z.
⇒ cot 30° = cot 210° = cot 390°, and so on.
Note: Since, cotangent is an odd function, the value of cot(30°) = cot(30°).
Methods to Find Value of Cot 30 Degrees
The cotangent function is positive in the 1st quadrant. The value of cot 30° is given as 1.73205. . . We can find the value of cot 30 degrees by:
 Using Trigonometric Functions
 Using Unit Circle
Cot 30° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cot 30 degrees as:
 cos(30°)/sin(30°)
 ± cos 30°/√(1  cos²(30°))
 ± √(1  sin²(30°))/sin 30°
 ± 1/√(sec²(30°)  1)
 ± √(cosec²(30°)  1)
 1/tan 30°
Note: Since 30° lies in the 1st Quadrant, the final value of cot 30° will be positive.
We can use trigonometric identities to represent cot 30° as,
 tan (90°  30°) = tan 60°
 tan (90° + 30°) = tan 120°
 cot (180°  30°) = cot 150°
Cot 30 Degrees Using Unit Circle
To find the value of cot 30 degrees using the unit circle:
 Rotate ‘r’ anticlockwise to form 30° angle with the positive xaxis.
 The cot of 30 degrees 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 30° = x/y = 1.7321 (approx).
☛ Also Check:
Examples Using Cot 30 Degrees

Example 1: Find the value of (cos (30°) cosec (15°) sec (15°))/2. [Hint: Use cot 30° = 1.7321]
Solution:
Using trigonometry formulas,
(cos (30°) cosec (15°) sec (15°))/2 = cos (30°)/(2 sin (15°) cos (15°))
Using sin 2a formula,
2 sin (15°) cos (15°) = sin (2 × 15°) = sin 30°
⇒ cos (30°) / sin (30°) = cot 30°
⇒ (cos (30°) cosec (15°) sec (15°))/2 = 1.7321 
Example 2: Find the value of 3 cot(30°)/7 cot(150°).
Solution:
Using trigonometric identities, we know, cot(30°) = cot(180°  30°) = cot 150°.
⇒ cot(30°) = cot(150°)
⇒ Value of 3 cot(30°)/7 cot(150°) = 3/7 
Example 3: Using the value of cot 30°, solve: (cosec²(30°)  1).
Solution:
We know, (cosec²(30°)  1) = (cot²(30°)) = 3
⇒ (cosec²(30°)  1) = 3
FAQs on Cot 30 Degrees
What is Cot 30 Degrees?
Cot 30 degrees is the value of cotangent trigonometric function for an angle equal to 30 degrees. The value of cot 30° is √3 or 1.7321 (approx).
What is the Exact Value of Cot 30 Degrees?
The exact value of cot 30 degrees can be given accurately up to 8 decimal places as 1.73205080 or as √3.
How to Find the Value of Cot 30 Degrees?
The value of cot 30 degrees can be calculated by constructing an angle of 30° with the xaxis, and then finding the coordinates of the corresponding point (0.866, 0.5) on the unit circle. The value of cot 30° is equal to the xcoordinate(0.866) divided by the ycoordinate (0.5). ∴ cot 30° = 1.7321
What is the Value of Cot 30 Degrees in Terms of Cos 30°?
We know, using trig identities, we can write cot 30° as cos 30°/√(1  cos²(30°)). Here, the value of cos 30° is equal to 0.866025.
How to Find Cot 30° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cot 30° can be given in terms of other trigonometric functions as:
 cos(30°)/sin(30°)
 ± cos 30°/√(1  cos²(30°))
 ± √(1  sin²(30°))/sin 30°
 ± 1/√(sec²(30°)  1)
 ± √(cosec²(30°)  1)
 1/tan 30°
☛ Also check: trigonometry table
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