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Cot 20 Degrees

The value of cot 20 degrees is 2.7474774. . .. Cot 20 degrees in radians is written as cot (20° × π/180°), i.e., cot (π/9) or cot (0.349065. . .). In this article, we will discuss the methods to find the value of cot 20 degrees with examples.

Cot 20° in decimal: 2.7474774. . .
Cot (-20 degrees): -2.7474774. . .
Cot 20° in radians: cot (π/9) or cot (0.3490658 . . .)

What is the Value of Cot 20 Degrees?

The value of cot 20 degrees in decimal is 2.747477419. . .. Cot 20 degrees can also be expressed using the equivalent of the given angle (20 degrees) in radians (0.34906 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 20 degrees = 20° × (π/180°) rad = π/9 or 0.3490 . . .
∴ cot 20° = cot(0.3490) = 2.7474774. . .

Explanation:

For cot 20 degrees, the angle 20° lies between 0° and 90° (First Quadrant). Since cotangent function is positive in the first quadrant, thus cot 20° value = 2.7474774. . .
Since the cotangent function is a periodic function, we can represent cot 20° as, cot 20 degrees = cot(20° + n × 180°), n ∈ Z.
⇒ cot 20° = cot 200° = cot 380°, and so on.
Note: Since, cotangent is an odd function, the value of cot(-20°) = -cot(20°).

Methods to Find Value of Cot 20 Degrees

The cotangent function is positive in the 1st quadrant. The value of cot 20° is given as 2.74747. . . We can find the value of cot 20 degrees by:

Using Trigonometric Functions
Using Unit Circle

Cot 20° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cot 20 degrees as:

cos(20°)/sin(20°)
± cos 20°/√(1 - cos²(20°))
± √(1 - sin²(20°))/sin 20°
± 1/√(sec²(20°) - 1)
± √(cosec²(20°) - 1)
1/tan 20°

Note: Since 20° lies in the 1st Quadrant, the final value of cot 20° will be positive.

We can use trigonometric identities to represent cot 20° as,

tan (90° - 20°) = tan 70°
-tan (90° + 20°) = -tan 110°
-cot (180° - 20°) = -cot 160°

Cot 20 Degrees Using Unit Circle

To find the value of cot 20 degrees using the unit circle:

Rotate ‘r’ anticlockwise to form 20° angle with the positive x-axis.
The cot of 20 degrees equals the x-coordinate(0.9397) divided by y-coordinate(0.342) of the point of intersection (0.9397, 0.342) of unit circle and r.

Hence the value of cot 20° = x/y = 2.7475 (approx).

☛ Also Check:

Examples Using Cot 20 Degrees

Example 1: Using the value of cot 20°, solve: (cosec²(20°) - 1).

Solution:
We know, (cosec²(20°) - 1) = (cot²(20°)) = 7.5486
⇒ (cosec²(20°) - 1) = 7.5486
Example 2: Find the value of (cos (20°) cosec (10°) sec (10°))/2. [Hint: Use cot 20° = 2.7475]

Solution:

Using trigonometry formulas,
(cos (20°) cosec (10°) sec (10°))/2 = cos (20°)/(2 sin (10°) cos (10°))
Using sin 2a formula,
2 sin (10°) cos (10°) = sin (2 × 10°) = sin 20°
⇒ cos (20°) / sin (20°) = cot 20°
⇒ (cos (20°) cosec (10°) sec (10°))/2 = 2.7475
Example 3: Simplify: 4 (cot 20°/tan 70°)

Solution:

We know cot 20° = tan 70°
⇒ 4 cot 20°/tan 70° = 4 (cot 20°/cot 20°)
= 4(1) = 4

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FAQs on Cot 20 Degrees

What is Cot 20 Degrees?

Cot 20 degrees is the value of cotangent trigonometric function for an angle equal to 20 degrees. The value of cot 20° is 2.7475 (approx).

What is the Exact Value of Cot 20 Degrees?

The exact value of cot 20 degrees can be given accurately up to 8 decimal places as 2.74747741.

What is the Value of Cot 20 Degrees in Terms of Tan 20°?

Since the cotangent function is the reciprocal of the tangent function, we can write cot 20° as 1/tan(20°). The value of tan 20° is equal to 0.36397.

How to Find Cot 20° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cot 20° can be given in terms of other trigonometric functions as:

cos(20°)/sin(20°)
± cos 20°/√(1 - cos²(20°))
± √(1 - sin²(20°))/sin 20°
± 1/√(sec²(20°) - 1)
± √(cosec²(20°) - 1)
1/tan 20°

☛ Also check: trigonometry table

How to Find the Value of Cot 20 Degrees?

The value of cot 20 degrees can be calculated by constructing an angle of 20° with the x-axis, and then finding the coordinates of the corresponding point (0.9397, 0.342) on the unit circle. The value of cot 20° is equal to the x-coordinate(0.9397) divided by the y-coordinate (0.342). ∴ cot 20° = 2.7475

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