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Cot 15 Degrees
The value of cot 15 degrees is 3.7320508. . .. Cot 15 degrees in radians is written as cot (15° × π/180°), i.e., cot (π/12) or cot (0.261799. . .). In this article, we will discuss the methods to find the value of cot 15 degrees with examples.
 Cot 15°: 2 + √3
 Cot 15° in decimal: 3.7320508. . .
 Cot (15 degrees): 3.7320508. . . or (2 + √3)
 Cot 15° in radians: cot (π/12) or cot (0.2617993 . . .)
What is the Value of Cot 15 Degrees?
The value of cot 15 degrees in decimal is 3.732050807. . .. Cot 15 degrees can also be expressed using the equivalent of the given angle (15 degrees) in radians (0.26179 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 15 degrees = 15° × (π/180°) rad = π/12 or 0.2617 . . .
∴ cot 15° = cot(0.2617) = 2 + √3 or 3.7320508. . .
Explanation:
For cot 15 degrees, the angle 15° lies between 0° and 90° (First Quadrant). Since cotangent function is positive in the first quadrant, thus cot 15° value = 2 + √3 or 3.7320508. . .
Since the cotangent function is a periodic function, we can represent cot 15° as, cot 15 degrees = cot(15° + n × 180°), n ∈ Z.
⇒ cot 15° = cot 195° = cot 375°, and so on.
Note: Since, cotangent is an odd function, the value of cot(15°) = cot(15°).
Methods to Find Value of Cot 15 Degrees
The cotangent function is positive in the 1st quadrant. The value of cot 15° is given as 3.73205. . . We can find the value of cot 15 degrees by:
 Using Trigonometric Functions
 Using Unit Circle
Cot 15° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cot 15 degrees as:
 cos(15°)/sin(15°)
 ± cos 15°/√(1  cos²(15°))
 ± √(1  sin²(15°))/sin 15°
 ± 1/√(sec²(15°)  1)
 ± √(cosec²(15°)  1)
 1/tan 15°
Note: Since 15° lies in the 1st Quadrant, the final value of cot 15° will be positive.
We can use trigonometric identities to represent cot 15° as,
 tan (90°  15°) = tan 75°
 tan (90° + 15°) = tan 105°
 cot (180°  15°) = cot 165°
Cot 15 Degrees Using Unit Circle
To find the value of cot 15 degrees using the unit circle:
 Rotate ‘r’ anticlockwise to form 15° angle with the positive xaxis.
 The cot of 15 degrees equals the xcoordinate(0.9659) divided by ycoordinate(0.2588) of the point of intersection (0.9659, 0.2588) of unit circle and r.
Hence the value of cot 15° = x/y = 3.7321 (approx).
☛ Also Check:
Examples Using Cot 15 Degrees

Example 1: Find the value of cot 15° if tan 15° is 0.2679.
Solution:
Since, cot 15° = 1/tan 15°
⇒ cot 15° = 1/0.2679 = 3.7321 
Example 2: Using the value of cot 15°, solve: (cosec²(15°)  1).
Solution:
We know, (cosec²(15°)  1) = (cot²(15°)) = 13.9282
⇒ (cosec²(15°)  1) = 13.9282 
Example 3: Find the value of (cos (15°) cosec (7.5°) sec (7.5°))/2. [Hint: Use cot 15° = 3.7321]
Solution:
Using trigonometry formulas,
(cos (15°) cosec (7.5°) sec (7.5°))/2 = cos (15°)/(2 sin (7.5°) cos (7.5°))
Using sin 2a formula,
2 sin (7.5°) cos (7.5°) = sin (2 × 7.5°) = sin 15°
⇒ cos (15°) / sin (15°) = cot 15°
⇒ (cos (15°) cosec (7.5°) sec (7.5°))/2 = 3.7321
FAQs on Cot 15 Degrees
What is Cot 15 Degrees?
Cot 15 degrees is the value of cotangent trigonometric function for an angle equal to 15 degrees. The value of cot 15° is 2 + √3 or 3.7321 (approx).
What is the Value of Cot 15 Degrees in Terms of Sin 15°?
Using trigonometric identities, we can write cot 15° in terms of sin 15° as, cot(15°) = √(1  sin²(15°))/sin 15° . Here, the value of sin 15° is equal to (√6  √2)/4.
How to Find Cot 15° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cot 15° can be given in terms of other trigonometric functions as:
 cos(15°)/sin(15°)
 ± cos 15°/√(1  cos²(15°))
 ± √(1  sin²(15°))/sin 15°
 ± 1/√(sec²(15°)  1)
 ± √(cosec²(15°)  1)
 1/tan 15°
☛ Also check: trigonometric table
How to Find the Value of Cot 15 Degrees?
The value of cot 15 degrees can be calculated by constructing an angle of 15° with the xaxis, and then finding the coordinates of the corresponding point (0.9659, 0.2588) on the unit circle. The value of cot 15° is equal to the xcoordinate(0.9659) divided by the ycoordinate (0.2588). ∴ cot 15° = 3.7321
What is the Exact Value of Cot 15 Degrees?
The exact value of cot 15 degrees can be given accurately up to 8 decimal places as 3.73205080 or as 2 + √3.
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