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Cot 75 Degrees
The value of cot 75 degrees is 0.2679491. . .. Cot 75 degrees in radians is written as cot (75° × π/180°), i.e., cot (5π/12) or cot (1.308996. . .). In this article, we will discuss the methods to find the value of cot 75 degrees with examples.
 Cot 75°: 2  √3
 Cot 75° in decimal: 0.2679491. . .
 Cot (75 degrees): 0.2679491. . . or 2 + √3
 Cot 75° in radians: cot (5π/12) or cot (1.3089969 . . .)
What is the Value of Cot 75 Degrees?
The value of cot 75 degrees in decimal is 0.267949192. . .. Cot 75 degrees can also be expressed using the equivalent of the given angle (75 degrees) in radians (1.30899 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 75 degrees = 75° × (π/180°) rad = 5π/12 or 1.3089 . . .
∴ cot 75° = cot(1.3089) = 2  √3 or 0.2679491. . .
Explanation:
For cot 75 degrees, the angle 75° lies between 0° and 90° (First Quadrant). Since cotangent function is positive in the first quadrant, thus cot 75° value = 2  √3 or 0.2679491. . .
Since the cotangent function is a periodic function, we can represent cot 75° as, cot 75 degrees = cot(75° + n × 180°), n ∈ Z.
⇒ cot 75° = cot 255° = cot 435°, and so on.
Note: Since, cotangent is an odd function, the value of cot(75°) = cot(75°).
Methods to Find Value of Cot 75 Degrees
The cotangent function is positive in the 1st quadrant. The value of cot 75° is given as 0.26794. . . We can find the value of cot 75 degrees by:
 Using Unit Circle
 Using Trigonometric Functions
Cot 75 Degrees Using Unit Circle
To find the value of cot 75 degrees using the unit circle:
 Rotate ‘r’ anticlockwise to form 75° angle with the positive xaxis.
 The cot of 75 degrees equals the xcoordinate(0.2588) divided by ycoordinate(0.9659) of the point of intersection (0.2588, 0.9659) of unit circle and r.
Hence the value of cot 75° = x/y = 0.2679 (approx).
Cot 75° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cot 75 degrees as:
 cos(75°)/sin(75°)
 ± cos 75°/√(1  cos²(75°))
 ± √(1  sin²(75°))/sin 75°
 ± 1/√(sec²(75°)  1)
 ± √(cosec²(75°)  1)
 1/tan 75°
Note: Since 75° lies in the 1st Quadrant, the final value of cot 75° will be positive.
We can use trigonometric identities to represent cot 75° as,
 tan (90°  75°) = tan 15°
 tan (90° + 75°) = tan 165°
 cot (180°  75°) = cot 105°
☛ Also Check:
Examples Using Cot 75 Degrees

Example 1: Using the value of cot 75°, solve: (cosec²(75°)  1).
Solution:
We know, (cosec²(75°)  1) = (cot²(75°)) = 0.0718
⇒ (cosec²(75°)  1) = 0.0718 
Example 2: Find the value of (cos (75°) cosec (37.5°) sec (37.5°))/2. [Hint: Use cot 75° = 0.2679]
Solution:
Using trigonometry formulas,
(cos (75°) cosec (37.5°) sec (37.5°))/2 = cos (75°)/(2 sin (37.5°) cos (37.5°))
Using sin 2a formula,
2 sin (37.5°) cos (37.5°) = sin (2 × 37.5°) = sin 75°
⇒ cos (75°) / sin (75°) = cot 75°
⇒ (cos (75°) cosec (37.5°) sec (37.5°))/2 = 0.2679 
Example 3: Find the value of cot 75° if tan 75° is 3.7320.
Solution:
Since, cot 75° = 1/tan 75°
⇒ cot 75° = 1/3.7320 = 0.2679
FAQs on Cot 75 Degrees
What is Cot 75 Degrees?
Cot 75 degrees is the value of cotangent trigonometric function for an angle equal to 75 degrees. The value of cot 75° is 2  √3 or 0.2679 (approx).
How to Find the Value of Cot 75 Degrees?
The value of cot 75 degrees can be calculated by constructing an angle of 75° with the xaxis, and then finding the coordinates of the corresponding point (0.2588, 0.9659) on the unit circle. The value of cot 75° is equal to the xcoordinate(0.2588) divided by the ycoordinate (0.9659). ∴ cot 75° = 0.2679
What is the Value of Cot 75° in Terms of Sec 75°?
We can represent the cotangent function in terms of the secant function using trig identities, cot 75° can be written as 1/√(sec²(75°)  1). Here, the value of sec 75° is equal to 3.8637.
What is the Value of Cot 75 Degrees in Terms of Tan 75°?
Since the cotangent function is the reciprocal of the tangent function, we can write cot 75° as 1/tan(75°). The value of tan 75° is equal to 2 + √3.
How to Find Cot 75° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cot 75° can be given in terms of other trigonometric functions as:
 cos(75°)/sin(75°)
 ± cos 75°/√(1  cos²(75°))
 ± √(1  sin²(75°))/sin 75°
 ± 1/√(sec²(75°)  1)
 ± √(cosec²(75°)  1)
 1/tan 75°
☛ Also check: trigonometry table
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