Cot 40 Degrees
The value of cot 40 degrees is 1.1917535. . .. Cot 40 degrees in radians is written as cot (40° × π/180°), i.e., cot (2π/9) or cot (0.698131. . .). In this article, we will discuss the methods to find the value of cot 40 degrees with examples.
 Cot 40° in decimal: 1.1917535. . .
 Cot (40 degrees): 1.1917535. . .
 Cot 40° in radians: cot (2π/9) or cot (0.6981317 . . .)
What is the Value of Cot 40 Degrees?
The value of cot 40 degrees in decimal is 1.191753592. . .. Cot 40 degrees can also be expressed using the equivalent of the given angle (40 degrees) in radians (0.69813 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 40 degrees = 40° × (π/180°) rad = 2π/9 or 0.6981 . . .
∴ cot 40° = cot(0.6981) = 1.1917535. . .
Explanation:
For cot 40 degrees, the angle 40° lies between 0° and 90° (First Quadrant). Since cotangent function is positive in the first quadrant, thus cot 40° value = 1.1917535. . .
Since the cotangent function is a periodic function, we can represent cot 40° as, cot 40 degrees = cot(40° + n × 180°), n ∈ Z.
⇒ cot 40° = cot 220° = cot 400°, and so on.
Note: Since, cotangent is an odd function, the value of cot(40°) = cot(40°).
Methods to Find Value of Cot 40 Degrees
The cotangent function is positive in the 1st quadrant. The value of cot 40° is given as 1.19175. . . We can find the value of cot 40 degrees by:
 Using Unit Circle
 Using Trigonometric Functions
Cot 40 Degrees Using Unit Circle
To find the value of cot 40 degrees using the unit circle:
 Rotate ‘r’ anticlockwise to form 40° angle with the positive xaxis.
 The cot of 40 degrees equals the xcoordinate(0.766) divided by ycoordinate(0.6428) of the point of intersection (0.766, 0.6428) of unit circle and r.
Hence the value of cot 40° = x/y = 1.1918 (approx).
Cot 40° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cot 40 degrees as:
 cos(40°)/sin(40°)
 ± cos 40°/√(1  cos²(40°))
 ± √(1  sin²(40°))/sin 40°
 ± 1/√(sec²(40°)  1)
 ± √(cosec²(40°)  1)
 1/tan 40°
Note: Since 40° lies in the 1st Quadrant, the final value of cot 40° will be positive.
We can use trigonometric identities to represent cot 40° as,
 tan (90°  40°) = tan 50°
 tan (90° + 40°) = tan 130°
 cot (180°  40°) = cot 140°
☛ Also Check:
Examples Using Cot 40 Degrees

Example 1: Find the value of (cos (40°) cosec (20°) sec (20°))/2. [Hint: Use cot 40° = 1.1918]
Solution:
Using trigonometry formulas,
(cos (40°) cosec (20°) sec (20°))/2 = cos (40°)/(2 sin (20°) cos (20°))
Using sin 2a formula,
2 sin (20°) cos (20°) = sin (2 × 20°) = sin 40°
⇒ cos (40°) / sin (40°) = cot 40°
⇒ (cos (40°) cosec (20°) sec (20°))/2 = 1.1918 
Example 2: Simplify: 4 (cot 40°/tan 50°)
Solution:
We know cot 40° = tan 50°
⇒ 4 cot 40°/tan 50° = 4 (cot 40°/cot 40°)
= 4(1) = 4 
Example 3: Find the value of cot 40° if tan 40° is 0.8390.
Solution:
Since, cot 40° = 1/tan 40°
⇒ cot 40° = 1/0.8390 = 1.1918
FAQs on Cot 40 Degrees
What is Cot 40 Degrees?
Cot 40 degrees is the value of cotangent trigonometric function for an angle equal to 40 degrees. The value of cot 40° is 1.1918 (approx).
How to Find Cot 40° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cot 40° can be given in terms of other trigonometric functions as:
 cos(40°)/sin(40°)
 ± cos 40°/√(1  cos²(40°))
 ± √(1  sin²(40°))/sin 40°
 ± 1/√(sec²(40°)  1)
 ± √(cosec²(40°)  1)
 1/tan 40°
☛ Also check: trigonometry table
How to Find the Value of Cot 40 Degrees?
The value of cot 40 degrees can be calculated by constructing an angle of 40° with the xaxis, and then finding the coordinates of the corresponding point (0.766, 0.6428) on the unit circle. The value of cot 40° is equal to the xcoordinate(0.766) divided by the ycoordinate (0.6428). ∴ cot 40° = 1.1918
What is the Value of Cot 40 Degrees in Terms of Tan 40°?
Since the cotangent function is the reciprocal of the tangent function, we can write cot 40° as 1/tan(40°). The value of tan 40° is equal to 0.83909.
What is the Exact Value of Cot 40 Degrees?
The exact value of cot 40 degrees can be given accurately up to 8 decimal places as 1.19175359.
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