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Cot 12 Degrees

The value of cot 12 degrees is 4.7046301. . .. Cot 12 degrees in radians is written as cot (12° × π/180°), i.e., cot (π/15) or cot (0.209439. . .). In this article, we will discuss the methods to find the value of cot 12 degrees with examples.

Cot 12° in decimal: 4.7046301. . .
Cot (-12 degrees): -4.7046301. . .
Cot 12° in radians: cot (π/15) or cot (0.2094395 . . .)

What is the Value of Cot 12 Degrees?

The value of cot 12 degrees in decimal is 4.704630109. . .. Cot 12 degrees can also be expressed using the equivalent of the given angle (12 degrees) in radians (0.20943 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 12 degrees = 12° × (π/180°) rad = π/15 or 0.2094 . . .
∴ cot 12° = cot(0.2094) = 4.7046301. . .

Explanation:

For cot 12 degrees, the angle 12° lies between 0° and 90° (First Quadrant). Since cotangent function is positive in the first quadrant, thus cot 12° value = 4.7046301. . .
Since the cotangent function is a periodic function, we can represent cot 12° as, cot 12 degrees = cot(12° + n × 180°), n ∈ Z.
⇒ cot 12° = cot 192° = cot 372°, and so on.
Note: Since, cotangent is an odd function, the value of cot(-12°) = -cot(12°).

Methods to Find Value of Cot 12 Degrees

The cotangent function is positive in the 1st quadrant. The value of cot 12° is given as 4.70463. . . We can find the value of cot 12 degrees by:

Using Unit Circle
Using Trigonometric Functions

Cot 12 Degrees Using Unit Circle

To find the value of cot 12 degrees using the unit circle:

Rotate ‘r’ anticlockwise to form 12° angle with the positive x-axis.
The cot of 12 degrees equals the x-coordinate(0.9781) divided by y-coordinate(0.2079) of the point of intersection (0.9781, 0.2079) of unit circle and r.

Hence the value of cot 12° = x/y = 4.7046 (approx).

Cot 12° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cot 12 degrees as:

cos(12°)/sin(12°)
± cos 12°/√(1 - cos²(12°))
± √(1 - sin²(12°))/sin 12°
± 1/√(sec²(12°) - 1)
± √(cosec²(12°) - 1)
1/tan 12°

Note: Since 12° lies in the 1st Quadrant, the final value of cot 12° will be positive.

We can use trigonometric identities to represent cot 12° as,

tan (90° - 12°) = tan 78°
-tan (90° + 12°) = -tan 102°
-cot (180° - 12°) = -cot 168°

☛ Also Check:

Examples Using Cot 12 Degrees

Example 1: Find the value of cot 12° if tan 12° is 0.2125.

Solution:
Since, cot 12° = 1/tan 12°
⇒ cot 12° = 1/0.2125 = 4.7046
Example 2: Find the value of (cos (12°) cosec (6°) sec (6°))/2. [Hint: Use cot 12° = 4.7046]

Solution:

Using trigonometry formulas,
(cos (12°) cosec (6°) sec (6°))/2 = cos (12°)/(2 sin (6°) cos (6°))
Using sin 2a formula,
2 sin (6°) cos (6°) = sin (2 × 6°) = sin 12°
⇒ cos (12°) / sin (12°) = cot 12°
⇒ (cos (12°) cosec (6°) sec (6°))/2 = 4.7046
Example 3: Using the value of cot 12°, solve: (cosec²(12°) - 1).

Solution:
We know, (cosec²(12°) - 1) = (cot²(12°)) = 22.1335
⇒ (cosec²(12°) - 1) = 22.1335

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FAQs on Cot 12 Degrees

What is Cot 12 Degrees?

Cot 12 degrees is the value of cotangent trigonometric function for an angle equal to 12 degrees. The value of cot 12° is 4.7046 (approx).

What is the Value of Cot 12° in Terms of Sec 12°?

We can represent the cotangent function in terms of the secant function using trig identities, cot 12° can be written as 1/√(sec²(12°) - 1). Here, the value of sec 12° is equal to 1.0223.

What is the Value of Cot 12 Degrees in Terms of Sin 12°?

Using trigonometric identities, we can write cot 12° in terms of sin 12° as, cot(12°) = √(1 - sin²(12°))/sin 12° . Here, the value of sin 12° is equal to 0.2079.

How to Find Cot 12° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cot 12° can be given in terms of other trigonometric functions as:

cos(12°)/sin(12°)
± cos 12°/√(1 - cos²(12°))
± √(1 - sin²(12°))/sin 12°
± 1/√(sec²(12°) - 1)
± √(cosec²(12°) - 1)
1/tan 12°

☛ Also check: trigonometric table

How to Find the Value of Cot 12 Degrees?

The value of cot 12 degrees can be calculated by constructing an angle of 12° with the x-axis, and then finding the coordinates of the corresponding point (0.9781, 0.2079) on the unit circle. The value of cot 12° is equal to the x-coordinate(0.9781) divided by the y-coordinate (0.2079). ∴ cot 12° = 4.7046

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