Cot 1 Degrees

The value of cot 1 degrees is 57.2899616. . .. Cot 1 degrees in radians is written as cot (1° × π/180°), i.e., cot (0.017453. . .). In this article, we will discuss the methods to find the value of cot 1 degrees with examples.

• Cot 1° in decimal: 57.2899616. . .
• Cot (-1 degrees): -57.2899616. . .
• Cot 1° in radians: cot (0.0174532 . . .)

What is the Value of Cot 1 Degrees?

The value of cot 1 degrees in decimal is 57.289961630. . .. Cot 1 degrees can also be expressed using the equivalent of the given angle (1 degrees) in radians (0.01745 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 1 degrees = 1° × (π/180°) rad = 0.0174 . . .
∴ cot 1° = cot(0.0174) = 57.2899616. . .

Explanation:

For cot 1 degrees, the angle 1° lies between 0° and 90° (First Quadrant). Since cotangent function is positive in the first quadrant, thus cot 1° value = 57.2899616. . .
Since the cotangent function is a periodic function, we can represent cot 1° as, cot 1 degrees = cot(1° + n × 180°), n ∈ Z.
⇒ cot 1° = cot 181° = cot 361°, and so on.
Note: Since, cotangent is an odd function, the value of cot(-1°) = -cot(1°).

Methods to Find Value of Cot 1 Degrees

The cotangent function is positive in the 1st quadrant. The value of cot 1° is given as 57.28996. . . We can find the value of cot 1 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Cot 1° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cot 1 degrees as:

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

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

We can use trigonometric identities to represent cot 1° as,

• tan (90° - 1°) = tan 89°
• -tan (90° + 1°) = -tan 91°
• -cot (180° - 1°) = -cot 179°

Cot 1 Degrees Using Unit Circle

To find the value of cot 1 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 1° angle with the positive x-axis.
• The cot of 1 degrees equals the x-coordinate(0.9998) divided by y-coordinate(0.0175) of the point of intersection (0.9998, 0.0175) of unit circle and r.

Hence the value of cot 1° = x/y = 57.29 (approx).

☛ Also Check:

• cot 37 degrees
• cot 60 degrees
• cot 13 degrees
• cot 150 degrees
• cot 4 degrees
• cot 330 degrees

FAQs on Cot 1 Degrees

What is Cot 1 Degrees?

Cot 1 degrees is the value of cotangent trigonometric function for an angle equal to 1 degrees. The value of cot 1° is 57.29 (approx).

How to Find the Value of Cot 1 Degrees?

The value of cot 1 degrees can be calculated by constructing an angle of 1° with the x-axis, and then finding the coordinates of the corresponding point (0.9998, 0.0175) on the unit circle. The value of cot 1° is equal to the x-coordinate(0.9998) divided by the y-coordinate (0.0175). ∴ cot 1° = 57.29

How to Find Cot 1° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cot 1° can be given in terms of other trigonometric functions as:

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

☛ Also check: trigonometric table

What is the Value of Cot 1 Degrees in Terms of Cos 1°?

We know, using trig identities, we can write cot 1° as cos 1°/√(1 - cos²(1°)). Here, the value of cos 1° is equal to 0.999847.

What is the Exact Value of Cot 1 Degrees?

The exact value of cot 1 degrees can be given accurately up to 8 decimal places as 57.28996163.