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Cot 25 Degrees
The value of cot 25 degrees is 2.1445069. . .. Cot 25 degrees in radians is written as cot (25° × π/180°), i.e., cot (5π/36) or cot (0.436332. . .). In this article, we will discuss the methods to find the value of cot 25 degrees with examples.
 Cot 25° in decimal: 2.1445069. . .
 Cot (25 degrees): 2.1445069. . .
 Cot 25° in radians: cot (5π/36) or cot (0.4363323 . . .)
What is the Value of Cot 25 Degrees?
The value of cot 25 degrees in decimal is 2.144506920. . .. Cot 25 degrees can also be expressed using the equivalent of the given angle (25 degrees) in radians (0.43633 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 25 degrees = 25° × (π/180°) rad = 5π/36 or 0.4363 . . .
∴ cot 25° = cot(0.4363) = 2.1445069. . .
Explanation:
For cot 25 degrees, the angle 25° lies between 0° and 90° (First Quadrant). Since cotangent function is positive in the first quadrant, thus cot 25° value = 2.1445069. . .
Since the cotangent function is a periodic function, we can represent cot 25° as, cot 25 degrees = cot(25° + n × 180°), n ∈ Z.
⇒ cot 25° = cot 205° = cot 385°, and so on.
Note: Since, cotangent is an odd function, the value of cot(25°) = cot(25°).
Methods to Find Value of Cot 25 Degrees
The cotangent function is positive in the 1st quadrant. The value of cot 25° is given as 2.14450. . . We can find the value of cot 25 degrees by:
 Using Trigonometric Functions
 Using Unit Circle
Cot 25° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cot 25 degrees as:
 cos(25°)/sin(25°)
 ± cos 25°/√(1  cos²(25°))
 ± √(1  sin²(25°))/sin 25°
 ± 1/√(sec²(25°)  1)
 ± √(cosec²(25°)  1)
 1/tan 25°
Note: Since 25° lies in the 1st Quadrant, the final value of cot 25° will be positive.
We can use trigonometric identities to represent cot 25° as,
 tan (90°  25°) = tan 65°
 tan (90° + 25°) = tan 115°
 cot (180°  25°) = cot 155°
Cot 25 Degrees Using Unit Circle
To find the value of cot 25 degrees using the unit circle:
 Rotate ‘r’ anticlockwise to form 25° angle with the positive xaxis.
 The cot of 25 degrees equals the xcoordinate(0.9063) divided by ycoordinate(0.4226) of the point of intersection (0.9063, 0.4226) of unit circle and r.
Hence the value of cot 25° = x/y = 2.1445 (approx).
☛ Also Check:
Examples Using Cot 25 Degrees

Example 1: Find the value of cot 25° if tan 25° is 0.4663.
Solution:
Since, cot 25° = 1/tan 25°
⇒ cot 25° = 1/0.4663 = 2.1445 
Example 2: Find the value of 4 cot(25°)/7 cot(155°).
Solution:
Using trigonometric identities, we know, cot(25°) = cot(180°  25°) = cot 155°.
⇒ cot(25°) = cot(155°)
⇒ Value of 4 cot(25°)/7 cot(155°) = 4/7 
Example 3: Find the value of (cos (25°) cosec (12.5°) sec (12.5°))/2. [Hint: Use cot 25° = 2.1445]
Solution:
Using trigonometry formulas,
(cos (25°) cosec (12.5°) sec (12.5°))/2 = cos (25°)/(2 sin (12.5°) cos (12.5°))
Using sin 2a formula,
2 sin (12.5°) cos (12.5°) = sin (2 × 12.5°) = sin 25°
⇒ cos (25°) / sin (25°) = cot 25°
⇒ (cos (25°) cosec (12.5°) sec (12.5°))/2 = 2.1445
FAQs on Cot 25 Degrees
What is Cot 25 Degrees?
Cot 25 degrees is the value of cotangent trigonometric function for an angle equal to 25 degrees. The value of cot 25° is 2.1445 (approx).
What is the Exact Value of Cot 25 Degrees?
The exact value of cot 25 degrees can be given accurately up to 8 decimal places as 2.14450692.
What is the Value of Cot 25 Degrees in Terms of Sin 25°?
Using trigonometric identities, we can write cot 25° in terms of sin 25° as, cot(25°) = √(1  sin²(25°))/sin 25° . Here, the value of sin 25° is equal to 0.4226.
How to Find Cot 25° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cot 25° can be given in terms of other trigonometric functions as:
 cos(25°)/sin(25°)
 ± cos 25°/√(1  cos²(25°))
 ± √(1  sin²(25°))/sin 25°
 ± 1/√(sec²(25°)  1)
 ± √(cosec²(25°)  1)
 1/tan 25°
☛ Also check: trigonometry table
How to Find the Value of Cot 25 Degrees?
The value of cot 25 degrees can be calculated by constructing an angle of 25° with the xaxis, and then finding the coordinates of the corresponding point (0.9063, 0.4226) on the unit circle. The value of cot 25° is equal to the xcoordinate(0.9063) divided by the ycoordinate (0.4226). ∴ cot 25° = 2.1445
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