Cot 3 Degrees

The value of cot 3 degrees is 19.0811366. . .. Cot 3 degrees in radians is written as cot (3° × π/180°), i.e., cot (π/60) or cot (0.052359. . .). In this article, we will discuss the methods to find the value of cot 3 degrees with examples.

• Cot 3° in decimal: 19.0811366. . .
• Cot (-3 degrees): -19.0811366. . .
• Cot 3° in radians: cot (π/60) or cot (0.0523598 . . .)

What is the Value of Cot 3 Degrees?

The value of cot 3 degrees in decimal is 19.081136687. . .. Cot 3 degrees can also be expressed using the equivalent of the given angle (3 degrees) in radians (0.05235 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 3 degrees = 3° × (π/180°) rad = π/60 or 0.0523 . . .
∴ cot 3° = cot(0.0523) = 19.0811366. . .

Explanation:

For cot 3 degrees, the angle 3° lies between 0° and 90° (First Quadrant). Since cotangent function is positive in the first quadrant, thus cot 3° value = 19.0811366. . .
Since the cotangent function is a periodic function, we can represent cot 3° as, cot 3 degrees = cot(3° + n × 180°), n ∈ Z.
⇒ cot 3° = cot 183° = cot 363°, and so on.
Note: Since, cotangent is an odd function, the value of cot(-3°) = -cot(3°).

Methods to Find Value of Cot 3 Degrees

The cotangent function is positive in the 1st quadrant. The value of cot 3° is given as 19.08113. . . We can find the value of cot 3 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Cot 3° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cot 3 degrees as:

• cos(3°)/sin(3°)
• ± cos 3°/√(1 - cos²(3°))
• ± √(1 - sin²(3°))/sin 3°
• ± 1/√(sec²(3°) - 1)
• ± √(cosec²(3°) - 1)
• 1/tan 3°

Note: Since 3° lies in the 1st Quadrant, the final value of cot 3° will be positive.

We can use trigonometric identities to represent cot 3° as,

• tan (90° - 3°) = tan 87°
• -tan (90° + 3°) = -tan 93°
• -cot (180° - 3°) = -cot 177°

Cot 3 Degrees Using Unit Circle

To find the value of cot 3 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 3° angle with the positive x-axis.
• The cot of 3 degrees equals the x-coordinate(0.9986) divided by y-coordinate(0.0523) of the point of intersection (0.9986, 0.0523) of unit circle and r.

Hence the value of cot 3° = x/y = 19.0811 (approx).

☛ Also Check:

• cot 570 degrees
• cot 20 degrees
• cot 7 degrees
• cot 3 degrees
• cot 600 degrees
• cot 136 degrees

FAQs on Cot 3 Degrees

What is Cot 3 Degrees?

Cot 3 degrees is the value of cotangent trigonometric function for an angle equal to 3 degrees. The value of cot 3° is 19.0811 (approx).

What is the Value of Cot 3 Degrees in Terms of Tan 3°?

Since the cotangent function is the reciprocal of the tangent function, we can write cot 3° as 1/tan(3°). The value of tan 3° is equal to 0.05240.

How to Find the Value of Cot 3 Degrees?

The value of cot 3 degrees can be calculated by constructing an angle of 3° with the x-axis, and then finding the coordinates of the corresponding point (0.9986, 0.0523) on the unit circle. The value of cot 3° is equal to the x-coordinate(0.9986) divided by the y-coordinate (0.0523). ∴ cot 3° = 19.0811

What is the Exact Value of Cot 3 Degrees?

The exact value of cot 3 degrees can be given accurately up to 8 decimal places as 19.08113668.

How to Find Cot 3° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cot 3° can be given in terms of other trigonometric functions as:

• cos(3°)/sin(3°)
• ± cos 3°/√(1 - cos²(3°))
• ± √(1 - sin²(3°))/sin 3°
• ± 1/√(sec²(3°) - 1)
• ± √(cosec²(3°) - 1)
• 1/tan 3°

☛ Also check: trigonometry table