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 x-axis.
• The cot of 4 degrees equals the x-coordinate(0.9976) divided by y-coordinate(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:

• cot 45 degrees
• cot 12 degrees
• cot 238 degrees
• cot 570 degrees
• cot 60 degrees
• cot 450 degrees

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 x-axis, 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 x-coordinate(0.9976) divided by the y-coordinate (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.