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Cot 9 Degrees

The value of cot 9 degrees is 6.3137515. . .. Cot 9 degrees in radians is written as cot (9° × π/180°), i.e., cot (π/20) or cot (0.157079. . .). In this article, we will discuss the methods to find the value of cot 9 degrees with examples.

Cot 9° in decimal: 6.3137515. . .
Cot (-9 degrees): -6.3137515. . .
Cot 9° in radians: cot (π/20) or cot (0.1570796 . . .)

What is the Value of Cot 9 Degrees?

The value of cot 9 degrees in decimal is 6.313751514. . .. Cot 9 degrees can also be expressed using the equivalent of the given angle (9 degrees) in radians (0.15707 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 9 degrees = 9° × (π/180°) rad = π/20 or 0.1570 . . .
∴ cot 9° = cot(0.1570) = 6.3137515. . .

Explanation:

For cot 9 degrees, the angle 9° lies between 0° and 90° (First Quadrant). Since cotangent function is positive in the first quadrant, thus cot 9° value = 6.3137515. . .
Since the cotangent function is a periodic function, we can represent cot 9° as, cot 9 degrees = cot(9° + n × 180°), n ∈ Z.
⇒ cot 9° = cot 189° = cot 369°, and so on.
Note: Since, cotangent is an odd function, the value of cot(-9°) = -cot(9°).

Methods to Find Value of Cot 9 Degrees

The cotangent function is positive in the 1st quadrant. The value of cot 9° is given as 6.31375. . . We can find the value of cot 9 degrees by:

Using Trigonometric Functions
Using Unit Circle

Cot 9° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cot 9 degrees as:

cos(9°)/sin(9°)
± cos 9°/√(1 - cos²(9°))
± √(1 - sin²(9°))/sin 9°
± 1/√(sec²(9°) - 1)
± √(cosec²(9°) - 1)
1/tan 9°

Note: Since 9° lies in the 1st Quadrant, the final value of cot 9° will be positive.

We can use trigonometric identities to represent cot 9° as,

tan (90° - 9°) = tan 81°
-tan (90° + 9°) = -tan 99°
-cot (180° - 9°) = -cot 171°

Cot 9 Degrees Using Unit Circle

To find the value of cot 9 degrees using the unit circle:

Rotate ‘r’ anticlockwise to form 9° angle with the positive x-axis.
The cot of 9 degrees equals the x-coordinate(0.9877) divided by y-coordinate(0.1564) of the point of intersection (0.9877, 0.1564) of unit circle and r.

Hence the value of cot 9° = x/y = 6.3138 (approx).

☛ Also Check:

Examples Using Cot 9 Degrees

Example 1: Find the value of (cos (9°) cosec (4.5°) sec (4.5°))/2. [Hint: Use cot 9° = 6.3138]

Solution:

Using trigonometry formulas,
(cos (9°) cosec (4.5°) sec (4.5°))/2 = cos (9°)/(2 sin (4.5°) cos (4.5°))
Using sin 2a formula,
2 sin (4.5°) cos (4.5°) = sin (2 × 4.5°) = sin 9°
⇒ cos (9°) / sin (9°) = cot 9°
⇒ (cos (9°) cosec (4.5°) sec (4.5°))/2 = 6.3138
Example 2: Find the value of 2 cot(9°)/4 cot(171°).

Solution:

Using trigonometric identities, we know, cot(9°) = -cot(180° - 9°) = -cot 171°.
⇒ cot(9°) = -cot(171°)
⇒ Value of 2 cot(9°)/4 cot(171°) = -2/4 = -1/2
Example 3: Using the value of cot 9°, solve: (cosec²(9°) - 1).

Solution:
We know, (cosec²(9°) - 1) = (cot²(9°)) = 39.8635
⇒ (cosec²(9°) - 1) = 39.8635

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FAQs on Cot 9 Degrees

What is Cot 9 Degrees?

Cot 9 degrees is the value of cotangent trigonometric function for an angle equal to 9 degrees. The value of cot 9° is 6.3138 (approx).

How to Find Cot 9° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cot 9° can be given in terms of other trigonometric functions as:

cos(9°)/sin(9°)
± cos 9°/√(1 - cos²(9°))
± √(1 - sin²(9°))/sin 9°
± 1/√(sec²(9°) - 1)
± √(cosec²(9°) - 1)
1/tan 9°

☛ Also check: trigonometric table

What is the Value of Cot 9 Degrees in Terms of Tan 9°?

Since the cotangent function is the reciprocal of the tangent function, we can write cot 9° as 1/tan(9°). The value of tan 9° is equal to 0.15838.

What is the Value of Cot 9° in Terms of Sec 9°?

We can represent the cotangent function in terms of the secant function using trig identities, cot 9° can be written as 1/√(sec²(9°) - 1). Here, the value of sec 9° is equal to 1.0124.

How to Find the Value of Cot 9 Degrees?

The value of cot 9 degrees can be calculated by constructing an angle of 9° with the x-axis, and then finding the coordinates of the corresponding point (0.9877, 0.1564) on the unit circle. The value of cot 9° is equal to the x-coordinate(0.9877) divided by the y-coordinate (0.1564). ∴ cot 9° = 6.3138

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