Cot 36 Degrees
The value of cot 36 degrees is 1.3763819. . .. Cot 36 degrees in radians is written as cot (36° × π/180°), i.e., cot (π/5) or cot (0.628318. . .). In this article, we will discuss the methods to find the value of cot 36 degrees with examples.
- Cot 36°: √(25 + 10√5)/5
- Cot 36° in decimal: 1.3763819. . .
- Cot (-36 degrees): -1.3763819. . .
- Cot 36° in radians: cot (π/5) or cot (0.6283185 . . .)
What is the Value of Cot 36 Degrees?
The value of cot 36 degrees in decimal is 1.376381920. . .. Cot 36 degrees can also be expressed using the equivalent of the given angle (36 degrees) in radians (0.62831 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 36 degrees = 36° × (π/180°) rad = π/5 or 0.6283 . . .
∴ cot 36° = cot(0.6283) = √(25 + 10√5)/5 or 1.3763819. . .
Explanation:
For cot 36 degrees, the angle 36° lies between 0° and 90° (First Quadrant). Since cotangent function is positive in the first quadrant, thus cot 36° value = √(25 + 10√5)/5 or 1.3763819. . .
Since the cotangent function is a periodic function, we can represent cot 36° as, cot 36 degrees = cot(36° + n × 180°), n ∈ Z.
⇒ cot 36° = cot 216° = cot 396°, and so on.
Note: Since, cotangent is an odd function, the value of cot(-36°) = -cot(36°).
Methods to Find Value of Cot 36 Degrees
The cotangent function is positive in the 1st quadrant. The value of cot 36° is given as 1.37638. . . We can find the value of cot 36 degrees by:
- Using Trigonometric Functions
- Using Unit Circle
Cot 36° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cot 36 degrees as:
- cos(36°)/sin(36°)
- ± cos 36°/√(1 - cos²(36°))
- ± √(1 - sin²(36°))/sin 36°
- ± 1/√(sec²(36°) - 1)
- ± √(cosec²(36°) - 1)
- 1/tan 36°
Note: Since 36° lies in the 1st Quadrant, the final value of cot 36° will be positive.
We can use trigonometric identities to represent cot 36° as,
- tan (90° - 36°) = tan 54°
- -tan (90° + 36°) = -tan 126°
- -cot (180° - 36°) = -cot 144°
Cot 36 Degrees Using Unit Circle
To find the value of cot 36 degrees using the unit circle:
- Rotate ‘r’ anticlockwise to form 36° angle with the positive x-axis.
- The cot of 36 degrees equals the x-coordinate(0.809) divided by y-coordinate(0.5878) of the point of intersection (0.809, 0.5878) of unit circle and r.
Hence the value of cot 36° = x/y = 1.3764 (approx).
☛ Also Check:
FAQs on Cot 36 Degrees
What is Cot 36 Degrees?
Cot 36 degrees is the value of cotangent trigonometric function for an angle equal to 36 degrees. The value of cot 36° is √(25 + 10√5)/5 or 1.3764 (approx).
What is the Value of Cot 36 Degrees in Terms of Tan 36°?
Since the cotangent function is the reciprocal of the tangent function, we can write cot 36° as 1/tan(36°). The value of tan 36° is equal to √(5 - 2√5).
How to Find Cot 36° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cot 36° can be given in terms of other trigonometric functions as:
- cos(36°)/sin(36°)
- ± cos 36°/√(1 - cos²(36°))
- ± √(1 - sin²(36°))/sin 36°
- ± 1/√(sec²(36°) - 1)
- ± √(cosec²(36°) - 1)
- 1/tan 36°
☛ Also check: trigonometry table
What is the Exact Value of Cot 36 Degrees?
The exact value of cot 36 degrees can be given accurately up to 8 decimal places as 1.37638192 or as √(25 + 10√5)/5.
How to Find the Value of Cot 36 Degrees?
The value of cot 36 degrees can be calculated by constructing an angle of 36° with the x-axis, and then finding the coordinates of the corresponding point (0.809, 0.5878) on the unit circle. The value of cot 36° is equal to the x-coordinate(0.809) divided by the y-coordinate (0.5878). ∴ cot 36° = 1.3764