Cot 45 Degrees
The value of cot 45 degrees is 1. Cot 45 degrees in radians is written as cot (45° × π/180°), i.e., cot (π/4) or cot (0.785398. . .). In this article, we will discuss the methods to find the value of cot 45 degrees with examples.
 Cot 45°: 1
 Cot (45 degrees): 1
 Cot 45° in radians: cot (π/4) or cot (0.7853981 . . .)
What is the Value of Cot 45 Degrees?
The value of cot 45 degrees is 1. Cot 45 degrees can also be expressed using the equivalent of the given angle (45 degrees) in radians (0.78539 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 45 degrees = 45° × (π/180°) rad = π/4 or 0.7853 . . .
∴ cot 45° = cot(0.7853) = 1
Explanation:
For cot 45 degrees, the angle 45° lies between 0° and 90° (First Quadrant). Since cotangent function is positive in the first quadrant, thus cot 45° value = 1
Since the cotangent function is a periodic function, we can represent cot 45° as, cot 45 degrees = cot(45° + n × 180°), n ∈ Z.
⇒ cot 45° = cot 225° = cot 405°, and so on.
Note: Since, cotangent is an odd function, the value of cot(45°) = cot(45°).
Methods to Find Value of Cot 45 Degrees
The cotangent function is positive in the 1st quadrant. The value of cot 45° is given as 1. We can find the value of cot 45 degrees by:
 Using Trigonometric Functions
 Using Unit Circle
Cot 45° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cot 45 degrees as:
 cos(45°)/sin(45°)
 ± cos 45°/√(1  cos²(45°))
 ± √(1  sin²(45°))/sin 45°
 ± 1/√(sec²(45°)  1)
 ± √(cosec²(45°)  1)
 1/tan 45°
Note: Since 45° lies in the 1st Quadrant, the final value of cot 45° will be positive.
We can use trigonometric identities to represent cot 45° as,
 tan (90°  45°) = tan 45°
 tan (90° + 45°) = tan 135°
 cot (180°  45°) = cot 135°
Cot 45 Degrees Using Unit Circle
To find the value of cot 45 degrees using the unit circle:
 Rotate ‘r’ anticlockwise to form 45° angle with the positive xaxis.
 The cot of 45 degrees equals the xcoordinate(0.7071) divided by ycoordinate(0.7071) of the point of intersection (0.7071, 0.7071) of unit circle and r.
Hence the value of cot 45° = x/y = 1
☛ Also Check:
Examples Using Cot 45 Degrees

Example 1: Using the value of cot 45°, solve: (cosec²(45°)  1).
Solution:
We know, (cosec²(45°)  1) = (cot²(45°)) = 1
⇒ (cosec²(45°)  1) = 1 
Example 2: Find the value of (cos (45°) cosec (22.5°) sec (22.5°))/2. [Hint: Use cot 45° = 1]
Solution:
Using trigonometry formulas,
(cos (45°) cosec (22.5°) sec (22.5°))/2 = cos (45°)/(2 sin (22.5°) cos (22.5°))
Using sin 2a formula,
2 sin (22.5°) cos (22.5°) = sin (2 × 22.5°) = sin 45°
⇒ cos (45°) / sin (45°) = cot 45°
⇒ (cos (45°) cosec (22.5°) sec (22.5°))/2 = 1 
Example 3: Simplify: 8 (cot 45°/tan 45°)
Solution:
We know cot 45° = tan 45°
⇒ 8 cot 45°/tan 45° = 8 (cot 45°/cot 45°)
= 8(1) = 8
FAQs on Cot 45 Degrees
What is Cot 45 Degrees?
Cot 45 degrees is the value of cotangent trigonometric function for an angle equal to 45 degrees. The value of cot 45° is 1.
How to Find the Value of Cot 45 Degrees?
The value of cot 45 degrees can be calculated by constructing an angle of 45° with the xaxis, and then finding the coordinates of the corresponding point (0.7071, 0.7071) on the unit circle. The value of cot 45° is equal to the xcoordinate(0.7071) divided by the ycoordinate (0.7071). ∴ cot 45° = 1
How to Find Cot 45° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cot 45° can be given in terms of other trigonometric functions as:
 cos(45°)/sin(45°)
 ± cos 45°/√(1  cos²(45°))
 ± √(1  sin²(45°))/sin 45°
 ± 1/√(sec²(45°)  1)
 ± √(cosec²(45°)  1)
 1/tan 45°
☛ Also check: trigonometric table
What is the Value of Cot 45° in Terms of Cosec 45°?
Since the cotangent function can be represented using the cosecant function, we can write cot 45° as √(cosec²(45°)  1). The value of cosec 45° is equal to 1.41421.
What is the Value of Cot 45 Degrees in Terms of Sin 45°?
Using trigonometric identities, we can write cot 45° in terms of sin 45° as, cot(45°) = √(1  sin²(45°))/sin 45° . Here, the value of sin 45° is equal to 1/√2.
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