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Cot 10 Degrees
The value of cot 10 degrees is 5.6712818. . .. Cot 10 degrees in radians is written as cot (10° × π/180°), i.e., cot (π/18) or cot (0.174532. . .). In this article, we will discuss the methods to find the value of cot 10 degrees with examples.
 Cot 10° in decimal: 5.6712818. . .
 Cot (10 degrees): 5.6712818. . .
 Cot 10° in radians: cot (π/18) or cot (0.1745329 . . .)
What is the Value of Cot 10 Degrees?
The value of cot 10 degrees in decimal is 5.671281819. . .. Cot 10 degrees can also be expressed using the equivalent of the given angle (10 degrees) in radians (0.17453 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 10 degrees = 10° × (π/180°) rad = π/18 or 0.1745 . . .
∴ cot 10° = cot(0.1745) = 5.6712818. . .
Explanation:
For cot 10 degrees, the angle 10° lies between 0° and 90° (First Quadrant). Since cotangent function is positive in the first quadrant, thus cot 10° value = 5.6712818. . .
Since the cotangent function is a periodic function, we can represent cot 10° as, cot 10 degrees = cot(10° + n × 180°), n ∈ Z.
⇒ cot 10° = cot 190° = cot 370°, and so on.
Note: Since, cotangent is an odd function, the value of cot(10°) = cot(10°).
Methods to Find Value of Cot 10 Degrees
The cotangent function is positive in the 1st quadrant. The value of cot 10° is given as 5.67128. . . We can find the value of cot 10 degrees by:
 Using Unit Circle
 Using Trigonometric Functions
Cot 10 Degrees Using Unit Circle
To find the value of cot 10 degrees using the unit circle:
 Rotate ‘r’ anticlockwise to form 10° angle with the positive xaxis.
 The cot of 10 degrees equals the xcoordinate(0.9848) divided by ycoordinate(0.1736) of the point of intersection (0.9848, 0.1736) of unit circle and r.
Hence the value of cot 10° = x/y = 5.6713 (approx).
Cot 10° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cot 10 degrees as:
 cos(10°)/sin(10°)
 ± cos 10°/√(1  cos²(10°))
 ± √(1  sin²(10°))/sin 10°
 ± 1/√(sec²(10°)  1)
 ± √(cosec²(10°)  1)
 1/tan 10°
Note: Since 10° lies in the 1st Quadrant, the final value of cot 10° will be positive.
We can use trigonometric identities to represent cot 10° as,
 tan (90°  10°) = tan 80°
 tan (90° + 10°) = tan 100°
 cot (180°  10°) = cot 170°
☛ Also Check:
Examples Using Cot 10 Degrees

Example 1: Find the value of cot 10° if tan 10° is 0.1763.
Solution:
Since, cot 10° = 1/tan 10°
⇒ cot 10° = 1/0.1763 = 5.6713 
Example 2: Simplify: 8 (cot 10°/tan 80°)
Solution:
We know cot 10° = tan 80°
⇒ 8 cot 10°/tan 80° = 8 (cot 10°/cot 10°)
= 8(1) = 8 
Example 3: Find the value of (cos (10°) cosec (5°) sec (5°))/2. [Hint: Use cot 10° = 5.6713]
Solution:
Using trigonometry formulas,
(cos (10°) cosec (5°) sec (5°))/2 = cos (10°)/(2 sin (5°) cos (5°))
Using sin 2a formula,
2 sin (5°) cos (5°) = sin (2 × 5°) = sin 10°
⇒ cos (10°) / sin (10°) = cot 10°
⇒ (cos (10°) cosec (5°) sec (5°))/2 = 5.6713
FAQs on Cot 10 Degrees
What is Cot 10 Degrees?
Cot 10 degrees is the value of cotangent trigonometric function for an angle equal to 10 degrees. The value of cot 10° is 5.6713 (approx).
What is the Exact Value of Cot 10 Degrees?
The exact value of cot 10 degrees can be given accurately up to 8 decimal places as 5.67128181.
How to Find the Value of Cot 10 Degrees?
The value of cot 10 degrees can be calculated by constructing an angle of 10° with the xaxis, and then finding the coordinates of the corresponding point (0.9848, 0.1736) on the unit circle. The value of cot 10° is equal to the xcoordinate(0.9848) divided by the ycoordinate (0.1736). ∴ cot 10° = 5.6713
What is the Value of Cot 10 Degrees in Terms of Cos 10°?
We know, using trig identities, we can write cot 10° as cos 10°/√(1  cos²(10°)). Here, the value of cos 10° is equal to 0.984807.
How to Find Cot 10° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cot 10° can be given in terms of other trigonometric functions as:
 cos(10°)/sin(10°)
 ± cos 10°/√(1  cos²(10°))
 ± √(1  sin²(10°))/sin 10°
 ± 1/√(sec²(10°)  1)
 ± √(cosec²(10°)  1)
 1/tan 10°
☛ Also check: trigonometry table
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