Cot 9 Degrees
The value of cot 9 degrees is 6.3137515. . .. Cot 9 degrees in radians is written as cot (9° × π/180°), i.e., cot (π/20) or cot (0.157079. . .). In this article, we will discuss the methods to find the value of cot 9 degrees with examples.
 Cot 9° in decimal: 6.3137515. . .
 Cot (9 degrees): 6.3137515. . .
 Cot 9° in radians: cot (π/20) or cot (0.1570796 . . .)
What is the Value of Cot 9 Degrees?
The value of cot 9 degrees in decimal is 6.313751514. . .. Cot 9 degrees can also be expressed using the equivalent of the given angle (9 degrees) in radians (0.15707 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 9 degrees = 9° × (π/180°) rad = π/20 or 0.1570 . . .
∴ cot 9° = cot(0.1570) = 6.3137515. . .
Explanation:
For cot 9 degrees, the angle 9° lies between 0° and 90° (First Quadrant). Since cotangent function is positive in the first quadrant, thus cot 9° value = 6.3137515. . .
Since the cotangent function is a periodic function, we can represent cot 9° as, cot 9 degrees = cot(9° + n × 180°), n ∈ Z.
⇒ cot 9° = cot 189° = cot 369°, and so on.
Note: Since, cotangent is an odd function, the value of cot(9°) = cot(9°).
Methods to Find Value of Cot 9 Degrees
The cotangent function is positive in the 1st quadrant. The value of cot 9° is given as 6.31375. . . We can find the value of cot 9 degrees by:
 Using Trigonometric Functions
 Using Unit Circle
Cot 9° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cot 9 degrees as:
 cos(9°)/sin(9°)
 ± cos 9°/√(1  cos²(9°))
 ± √(1  sin²(9°))/sin 9°
 ± 1/√(sec²(9°)  1)
 ± √(cosec²(9°)  1)
 1/tan 9°
Note: Since 9° lies in the 1st Quadrant, the final value of cot 9° will be positive.
We can use trigonometric identities to represent cot 9° as,
 tan (90°  9°) = tan 81°
 tan (90° + 9°) = tan 99°
 cot (180°  9°) = cot 171°
Cot 9 Degrees Using Unit Circle
To find the value of cot 9 degrees using the unit circle:
 Rotate ‘r’ anticlockwise to form 9° angle with the positive xaxis.
 The cot of 9 degrees equals the xcoordinate(0.9877) divided by ycoordinate(0.1564) of the point of intersection (0.9877, 0.1564) of unit circle and r.
Hence the value of cot 9° = x/y = 6.3138 (approx).
☛ Also Check:
Examples Using Cot 9 Degrees

Example 1: Find the value of (cos (9°) cosec (4.5°) sec (4.5°))/2. [Hint: Use cot 9° = 6.3138]
Solution:
Using trigonometry formulas,
(cos (9°) cosec (4.5°) sec (4.5°))/2 = cos (9°)/(2 sin (4.5°) cos (4.5°))
Using sin 2a formula,
2 sin (4.5°) cos (4.5°) = sin (2 × 4.5°) = sin 9°
⇒ cos (9°) / sin (9°) = cot 9°
⇒ (cos (9°) cosec (4.5°) sec (4.5°))/2 = 6.3138 
Example 2: Find the value of 2 cot(9°)/4 cot(171°).
Solution:
Using trigonometric identities, we know, cot(9°) = cot(180°  9°) = cot 171°.
⇒ cot(9°) = cot(171°)
⇒ Value of 2 cot(9°)/4 cot(171°) = 2/4 = 1/2 
Example 3: Using the value of cot 9°, solve: (cosec²(9°)  1).
Solution:
We know, (cosec²(9°)  1) = (cot²(9°)) = 39.8635
⇒ (cosec²(9°)  1) = 39.8635
FAQs on Cot 9 Degrees
What is Cot 9 Degrees?
Cot 9 degrees is the value of cotangent trigonometric function for an angle equal to 9 degrees. The value of cot 9° is 6.3138 (approx).
How to Find Cot 9° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cot 9° can be given in terms of other trigonometric functions as:
 cos(9°)/sin(9°)
 ± cos 9°/√(1  cos²(9°))
 ± √(1  sin²(9°))/sin 9°
 ± 1/√(sec²(9°)  1)
 ± √(cosec²(9°)  1)
 1/tan 9°
☛ Also check: trigonometric table
What is the Value of Cot 9 Degrees in Terms of Tan 9°?
Since the cotangent function is the reciprocal of the tangent function, we can write cot 9° as 1/tan(9°). The value of tan 9° is equal to 0.15838.
What is the Value of Cot 9° in Terms of Sec 9°?
We can represent the cotangent function in terms of the secant function using trig identities, cot 9° can be written as 1/√(sec²(9°)  1). Here, the value of sec 9° is equal to 1.0124.
How to Find the Value of Cot 9 Degrees?
The value of cot 9 degrees can be calculated by constructing an angle of 9° with the xaxis, and then finding the coordinates of the corresponding point (0.9877, 0.1564) on the unit circle. The value of cot 9° is equal to the xcoordinate(0.9877) divided by the ycoordinate (0.1564). ∴ cot 9° = 6.3138
visual curriculum