Cot 5 Degrees

The value of cot 5 degrees is 11.4300523. . .. Cot 5 degrees in radians is written as cot (5° × π/180°), i.e., cot (π/36) or cot (0.087266. . .). In this article, we will discuss the methods to find the value of cot 5 degrees with examples.

• Cot 5° in decimal: 11.4300523. . .
• Cot (-5 degrees): -11.4300523. . .
• Cot 5° in radians: cot (π/36) or cot (0.0872664 . . .)

What is the Value of Cot 5 Degrees?

The value of cot 5 degrees in decimal is 11.430052302. . .. Cot 5 degrees can also be expressed using the equivalent of the given angle (5 degrees) in radians (0.08726 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 5 degrees = 5° × (π/180°) rad = π/36 or 0.0872 . . .
∴ cot 5° = cot(0.0872) = 11.4300523. . .

Explanation:

For cot 5 degrees, the angle 5° lies between 0° and 90° (First Quadrant). Since cotangent function is positive in the first quadrant, thus cot 5° value = 11.4300523. . .
Since the cotangent function is a periodic function, we can represent cot 5° as, cot 5 degrees = cot(5° + n × 180°), n ∈ Z.
⇒ cot 5° = cot 185° = cot 365°, and so on.
Note: Since, cotangent is an odd function, the value of cot(-5°) = -cot(5°).

Methods to Find Value of Cot 5 Degrees

The cotangent function is positive in the 1st quadrant. The value of cot 5° is given as 11.43005. . . We can find the value of cot 5 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Cot 5 Degrees Using Unit Circle

To find the value of cot 5 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 5° angle with the positive x-axis.
• The cot of 5 degrees equals the x-coordinate(0.9962) divided by y-coordinate(0.0872) of the point of intersection (0.9962, 0.0872) of unit circle and r.

Hence the value of cot 5° = x/y = 11.4301 (approx).

Cot 5° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cot 5 degrees as:

• cos(5°)/sin(5°)
• ± cos 5°/√(1 - cos²(5°))
• ± √(1 - sin²(5°))/sin 5°
• ± 1/√(sec²(5°) - 1)
• ± √(cosec²(5°) - 1)
• 1/tan 5°

Note: Since 5° lies in the 1st Quadrant, the final value of cot 5° will be positive.

We can use trigonometric identities to represent cot 5° as,

• tan (90° - 5°) = tan 85°
• -tan (90° + 5°) = -tan 95°
• -cot (180° - 5°) = -cot 175°

☛ Also Check:

• cot 18 degrees
• cot 5 degrees
• cot 239 degrees
• cot 238 degrees
• cot 105 degrees
• cot 315 degrees

FAQs on Cot 5 Degrees

What is Cot 5 Degrees?

Cot 5 degrees is the value of cotangent trigonometric function for an angle equal to 5 degrees. The value of cot 5° is 11.4301 (approx).

What is the Value of Cot 5° in Terms of Cosec 5°?

Since the cotangent function can be represented using the cosecant function, we can write cot 5° as √(cosec²(5°) - 1). The value of cosec 5° is equal to 11.47371.

What is the Value of Cot 5 Degrees in Terms of Sin 5°?

Using trigonometric identities, we can write cot 5° in terms of sin 5° as, cot(5°) = √(1 - sin²(5°))/sin 5° . Here, the value of sin 5° is equal to 0.0872.

How to Find Cot 5° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cot 5° can be given in terms of other trigonometric functions as:

• cos(5°)/sin(5°)
• ± cos 5°/√(1 - cos²(5°))
• ± √(1 - sin²(5°))/sin 5°
• ± 1/√(sec²(5°) - 1)
• ± √(cosec²(5°) - 1)
• 1/tan 5°

☛ Also check: trigonometric table

How to Find the Value of Cot 5 Degrees?

The value of cot 5 degrees can be calculated by constructing an angle of 5° with the x-axis, and then finding the coordinates of the corresponding point (0.9962, 0.0872) on the unit circle. The value of cot 5° is equal to the x-coordinate(0.9962) divided by the y-coordinate (0.0872). ∴ cot 5° = 11.4301