Cot 11 Degrees
The value of cot 11 degrees is 5.1445540. . .. Cot 11 degrees in radians is written as cot (11° × π/180°), i.e., cot (0.191986. . .). In this article, we will discuss the methods to find the value of cot 11 degrees with examples.
 Cot 11° in decimal: 5.1445540. . .
 Cot (11 degrees): 5.1445540. . .
 Cot 11° in radians: cot (0.1919862 . . .)
What is the Value of Cot 11 Degrees?
The value of cot 11 degrees in decimal is 5.144554015. . .. Cot 11 degrees can also be expressed using the equivalent of the given angle (11 degrees) in radians (0.19198 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 11 degrees = 11° × (π/180°) rad = 0.1919 . . .
∴ cot 11° = cot(0.1919) = 5.1445540. . .
Explanation:
For cot 11 degrees, the angle 11° lies between 0° and 90° (First Quadrant). Since cotangent function is positive in the first quadrant, thus cot 11° value = 5.1445540. . .
Since the cotangent function is a periodic function, we can represent cot 11° as, cot 11 degrees = cot(11° + n × 180°), n ∈ Z.
⇒ cot 11° = cot 191° = cot 371°, and so on.
Note: Since, cotangent is an odd function, the value of cot(11°) = cot(11°).
Methods to Find Value of Cot 11 Degrees
The cotangent function is positive in the 1st quadrant. The value of cot 11° is given as 5.14455. . . We can find the value of cot 11 degrees by:
 Using Unit Circle
 Using Trigonometric Functions
Cot 11 Degrees Using Unit Circle
To find the value of cot 11 degrees using the unit circle:
 Rotate ‘r’ anticlockwise to form 11° angle with the positive xaxis.
 The cot of 11 degrees equals the xcoordinate(0.9816) divided by ycoordinate(0.1908) of the point of intersection (0.9816, 0.1908) of unit circle and r.
Hence the value of cot 11° = x/y = 5.1446 (approx).
Cot 11° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cot 11 degrees as:
 cos(11°)/sin(11°)
 ± cos 11°/√(1  cos²(11°))
 ± √(1  sin²(11°))/sin 11°
 ± 1/√(sec²(11°)  1)
 ± √(cosec²(11°)  1)
 1/tan 11°
Note: Since 11° lies in the 1st Quadrant, the final value of cot 11° will be positive.
We can use trigonometric identities to represent cot 11° as,
 tan (90°  11°) = tan 79°
 tan (90° + 11°) = tan 101°
 cot (180°  11°) = cot 169°
☛ Also Check:
Examples Using Cot 11 Degrees

Example 1: Using the value of cot 11°, solve: (cosec²(11°)  1).
Solution:
We know, (cosec²(11°)  1) = (cot²(11°)) = 26.4664
⇒ (cosec²(11°)  1) = 26.4664 
Example 2: Find the value of (cos (11°) cosec (5.5°) sec (5.5°))/2. [Hint: Use cot 11° = 5.1446]
Solution:
Using trigonometry formulas,
(cos (11°) cosec (5.5°) sec (5.5°))/2 = cos (11°)/(2 sin (5.5°) cos (5.5°))
Using sin 2a formula,
2 sin (5.5°) cos (5.5°) = sin (2 × 5.5°) = sin 11°
⇒ cos (11°) / sin (11°) = cot 11°
⇒ (cos (11°) cosec (5.5°) sec (5.5°))/2 = 5.1446 
Example 3: Find the value of cot 11° if tan 11° is 0.1943.
Solution:
Since, cot 11° = 1/tan 11°
⇒ cot 11° = 1/0.1943 = 5.1446
FAQs on Cot 11 Degrees
What is Cot 11 Degrees?
Cot 11 degrees is the value of cotangent trigonometric function for an angle equal to 11 degrees. The value of cot 11° is 5.1446 (approx).
What is the Value of Cot 11 Degrees in Terms of Tan 11°?
Since the cotangent function is the reciprocal of the tangent function, we can write cot 11° as 1/tan(11°). The value of tan 11° is equal to 0.19438.
How to Find the Value of Cot 11 Degrees?
The value of cot 11 degrees can be calculated by constructing an angle of 11° with the xaxis, and then finding the coordinates of the corresponding point (0.9816, 0.1908) on the unit circle. The value of cot 11° is equal to the xcoordinate(0.9816) divided by the ycoordinate (0.1908). ∴ cot 11° = 5.1446
What is the Exact Value of Cot 11 Degrees?
The exact value of cot 11 degrees can be given accurately up to 8 decimal places as 5.14455401.
How to Find Cot 11° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cot 11° can be given in terms of other trigonometric functions as:
 cos(11°)/sin(11°)
 ± cos 11°/√(1  cos²(11°))
 ± √(1  sin²(11°))/sin 11°
 ± 1/√(sec²(11°)  1)
 ± √(cosec²(11°)  1)
 1/tan 11°
☛ Also check: trigonometry table