Cot 4 Degrees
The value of cot 4 degrees is 14.3006662. . .. Cot 4 degrees in radians is written as cot (4° × π/180°), i.e., cot (π/45) or cot (0.069813. . .). In this article, we will discuss the methods to find the value of cot 4 degrees with examples.
 Cot 4° in decimal: 14.3006662. . .
 Cot (4 degrees): 14.3006662. . .
 Cot 4° in radians: cot (π/45) or cot (0.0698131 . . .)
What is the Value of Cot 4 Degrees?
The value of cot 4 degrees in decimal is 14.300666256. . .. Cot 4 degrees can also be expressed using the equivalent of the given angle (4 degrees) in radians (0.06981 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 4 degrees = 4° × (π/180°) rad = π/45 or 0.0698 . . .
∴ cot 4° = cot(0.0698) = 14.3006662. . .
Explanation:
For cot 4 degrees, the angle 4° lies between 0° and 90° (First Quadrant). Since cotangent function is positive in the first quadrant, thus cot 4° value = 14.3006662. . .
Since the cotangent function is a periodic function, we can represent cot 4° as, cot 4 degrees = cot(4° + n × 180°), n ∈ Z.
⇒ cot 4° = cot 184° = cot 364°, and so on.
Note: Since, cotangent is an odd function, the value of cot(4°) = cot(4°).
Methods to Find Value of Cot 4 Degrees
The cotangent function is positive in the 1st quadrant. The value of cot 4° is given as 14.30066. . . We can find the value of cot 4 degrees by:
 Using Unit Circle
 Using Trigonometric Functions
Cot 4 Degrees Using Unit Circle
To find the value of cot 4 degrees using the unit circle:
 Rotate ‘r’ anticlockwise to form 4° angle with the positive xaxis.
 The cot of 4 degrees equals the xcoordinate(0.9976) divided by ycoordinate(0.0698) of the point of intersection (0.9976, 0.0698) of unit circle and r.
Hence the value of cot 4° = x/y = 14.3007 (approx).
Cot 4° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cot 4 degrees as:
 cos(4°)/sin(4°)
 ± cos 4°/√(1  cos²(4°))
 ± √(1  sin²(4°))/sin 4°
 ± 1/√(sec²(4°)  1)
 ± √(cosec²(4°)  1)
 1/tan 4°
Note: Since 4° lies in the 1st Quadrant, the final value of cot 4° will be positive.
We can use trigonometric identities to represent cot 4° as,
 tan (90°  4°) = tan 86°
 tan (90° + 4°) = tan 94°
 cot (180°  4°) = cot 176°
☛ Also Check:
Examples Using Cot 4 Degrees

Example 1: Find the value of 7 cot(4°)/9 cot(176°).
Solution:
Using trigonometric identities, we know, cot(4°) = cot(180°  4°) = cot 176°.
⇒ cot(4°) = cot(176°)
⇒ Value of 7 cot(4°)/9 cot(176°) = 7/9 
Example 2: Find the value of (cos (4°) cosec (2°) sec (2°))/2. [Hint: Use cot 4° = 14.3007]
Solution:
Using trigonometry formulas,
(cos (4°) cosec (2°) sec (2°))/2 = cos (4°)/(2 sin (2°) cos (2°))
Using sin 2a formula,
2 sin (2°) cos (2°) = sin (2 × 2°) = sin 4°
⇒ cos (4°) / sin (4°) = cot 4°
⇒ (cos (4°) cosec (2°) sec (2°))/2 = 14.3007 
Example 3: Simplify: 4 (cot 4°/tan 86°)
Solution:
We know cot 4° = tan 86°
⇒ 4 cot 4°/tan 86° = 4 (cot 4°/cot 4°)
= 4(1) = 4
FAQs on Cot 4 Degrees
What is Cot 4 Degrees?
Cot 4 degrees is the value of cotangent trigonometric function for an angle equal to 4 degrees. The value of cot 4° is 14.3007 (approx).
What is the Value of Cot 4° in Terms of Sec 4°?
We can represent the cotangent function in terms of the secant function using trig identities, cot 4° can be written as 1/√(sec²(4°)  1). Here, the value of sec 4° is equal to 1.0024.
How to Find Cot 4° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cot 4° can be given in terms of other trigonometric functions as:
 cos(4°)/sin(4°)
 ± cos 4°/√(1  cos²(4°))
 ± √(1  sin²(4°))/sin 4°
 ± 1/√(sec²(4°)  1)
 ± √(cosec²(4°)  1)
 1/tan 4°
☛ Also check: trigonometry table
How to Find the Value of Cot 4 Degrees?
The value of cot 4 degrees can be calculated by constructing an angle of 4° with the xaxis, and then finding the coordinates of the corresponding point (0.9976, 0.0698) on the unit circle. The value of cot 4° is equal to the xcoordinate(0.9976) divided by the ycoordinate (0.0698). ∴ cot 4° = 14.3007
What is the Value of Cot 4 Degrees in Terms of Cos 4°?
We know, using trig identities, we can write cot 4° as cos 4°/√(1  cos²(4°)). Here, the value of cos 4° is equal to 0.997564.
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