Cot 210 Degrees
The value of cot 210 degrees is 1.7320508. . .. Cot 210 degrees in radians is written as cot (210° × π/180°), i.e., cot (7π/6) or cot (3.665191. . .). In this article, we will discuss the methods to find the value of cot 210 degrees with examples.
 Cot 210°: √3
 Cot 210° in decimal: 1.7320508. . .
 Cot (210 degrees): 1.7320508. . . or √3
 Cot 210° in radians: cot (7π/6) or cot (3.6651914 . . .)
What is the Value of Cot 210 Degrees?
The value of cot 210 degrees in decimal is 1.732050807. . .. Cot 210 degrees can also be expressed using the equivalent of the given angle (210 degrees) in radians (3.66519 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 210 degrees = 210° × (π/180°) rad = 7π/6 or 3.6651 . . .
∴ cot 210° = cot(3.6651) = √3 or 1.7320508. . .
Explanation:
For cot 210 degrees, the angle 210° lies between 180° and 270° (Third Quadrant). Since cotangent function is positive in the third quadrant, thus cot 210° value = √3 or 1.7320508. . .
Since the cotangent function is a periodic function, we can represent cot 210° as, cot 210 degrees = cot(210° + n × 180°), n ∈ Z.
⇒ cot 210° = cot 390° = cot 570°, and so on.
Note: Since, cotangent is an odd function, the value of cot(210°) = cot(210°).
Methods to Find Value of Cot 210 Degrees
The cotangent function is positive in the 3rd quadrant. The value of cot 210° is given as 1.73205. . . We can find the value of cot 210 degrees by:
 Using Trigonometric Functions
 Using Unit Circle
Cot 210° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cot 210 degrees as:
 cos(210°)/sin(210°)
 ± cos 210°/√(1  cos²(210°))
 ± √(1  sin²(210°))/sin 210°
 ± 1/√(sec²(210°)  1)
 ± √(cosec²(210°)  1)
 1/tan 210°
Note: Since 210° lies in the 3rd Quadrant, the final value of cot 210° will be positive.
We can use trigonometric identities to represent cot 210° as,
 tan (90°  210°) = tan(120°)
 tan (90° + 210°) = tan 300°
 cot (180°  210°) = cot(30°)
Cot 210 Degrees Using Unit Circle
To find the value of cot 210 degrees using the unit circle:
 Rotate ‘r’ anticlockwise to form 210° angle with the positive xaxis.
 The cot of 210 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 210° = x/y = 1.7321 (approx).
☛ Also Check:
Examples Using Cot 210 Degrees

Example 1: Find the value of (cos (210°) cosec (105°) sec (105°))/2. [Hint: Use cot 210° = 1.7321]
Solution:
Using trigonometry formulas,
(cos (210°) cosec (105°) sec (105°))/2 = cos (210°)/(2 sin (105°) cos (105°))
Using sin 2a formula,
2 sin (105°) cos (105°) = sin (2 × 105°) = sin 210°
⇒ cos (210°) / sin (210°) = cot 210°
⇒ (cos (210°) cosec (105°) sec (105°))/2 = 1.7321 
Example 2: Find the value of cot 210° if tan 210° is 0.5773.
Solution:
Since, cot 210° = 1/tan 210°
⇒ cot 210° = 1/0.5773 = 1.7321 
Example 3: Using the value of cot 210°, solve: (cosec²(210°)  1).
Solution:
We know, (cosec²(210°)  1) = (cot²(210°)) = 3
⇒ (cosec²(210°)  1) = 3
FAQs on Cot 210 Degrees
What is Cot 210 Degrees?
Cot 210 degrees is the value of cotangent trigonometric function for an angle equal to 210 degrees. The value of cot 210° is √3 or 1.7321 (approx).
How to Find Cot 210° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cot 210° can be given in terms of other trigonometric functions as:
 cos(210°)/sin(210°)
 ± cos 210°/√(1  cos²(210°))
 ± √(1  sin²(210°))/sin 210°
 ± 1/√(sec²(210°)  1)
 ± √(cosec²(210°)  1)
 1/tan 210°
☛ Also check: trigonometric table
What is the Value of Cot 210 Degrees in Terms of Sin 210°?
Using trigonometric identities, we can write cot 210° in terms of sin 210° as, cot(210°) = √(1  sin²(210°))/sin 210° . Here, the value of sin 210° is equal to (1/2).
What is the Exact Value of Cot 210 Degrees?
The exact value of cot 210 degrees can be given accurately up to 8 decimal places as 1.73205080 or as √3.
How to Find the Value of Cot 210 Degrees?
The value of cot 210 degrees can be calculated by constructing an angle of 210° with the xaxis, and then finding the coordinates of the corresponding point (0.866, 0.5) on the unit circle. The value of cot 210° is equal to the xcoordinate(0.866) divided by the ycoordinate (0.5). ∴ cot 210° = 1.7321
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