Cot 450 Degrees
The value of cot 450 degrees is 0. Cot 450 degrees in radians is written as cot (450° × π/180°), i.e., cot (5π/2) or cot (7.853981. . .). In this article, we will discuss the methods to find the value of cot 450 degrees with examples.
 Cot 450°: 0
 Cot (450 degrees): 0
 Cot 450° in radians: cot (5π/2) or cot (7.8539816 . . .)
What is the Value of Cot 450 Degrees?
The value of cot 450 degrees is 0. Cot 450 degrees can also be expressed using the equivalent of the given angle (450 degrees) in radians (7.85398 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 450 degrees = 450° × (π/180°) rad = 5π/2 or 7.8539 . . .
∴ cot 450° = cot(7.8539) = 0
Explanation:
For cot 450°, the angle 450° > 360°. We can represent cot 450° as, cot(450° mod 360°) = cot(90°). The angle 450°, coterminal to angle 90°, lies on the positive yaxis.
Thus cot 450 degrees value = 0
Similarly, given the periodic property of cot 450°, it can also be written as, cot 450 degrees = (450° + n × 180°), n ∈ Z.
⇒ cot 450° = cot 630° = cot 810°, and so on.
Note: Since, cotangent is an odd function, the value of cot(450°) = cot(450°) = 0.
Methods to Find Value of Cot 450 Degrees
The value of cot 450° is given as 0. We can find the value of cot 450 degrees by:
 Using Unit Circle
 Using Trigonometric Functions
Cot 450 Degrees Using Unit Circle
To find the value of cot 450 degrees using the unit circle, represent 450° in the form (1 × 360°) + 90° [∵ 450°>360°] ∵ The angle 450° is coterminal to 90° angle and also cotangent is a periodic function, cot 450° = cot 90°.
 Rotate ‘r’ anticlockwise to form 90° or 450° angle with the positive xaxis.
 The cot of 450 degrees equals the xcoordinate(0) divided by ycoordinate(1) of the point of intersection (0, 1) of unit circle and r.
Hence the value of cot 450° = x/y = 0
Cot 450° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cot 450 degrees as:
 cos(450°)/sin(450°)
 ± cos 450°/√(1  cos²(450°))
 ± √(1  sin²(450°))/sin 450°
 ± 1/√(sec²(450°)  1)
 ± √(cosec²(450°)  1)
 1/tan 450°
Note: Since 450° lies on the positive yaxis, the final value of cot 450° is 0.
We can use trigonometric identities to represent cot 450° as,
 tan (90°  450°) = tan(360°)
 tan (90° + 450°) = tan 540°
 cot (180°  450°) = cot(270°)
☛ Also Check:
Examples Using Cot 450 Degrees

Example 1: Find the value of (cos (450°) cosec (225°) sec (225°))/2. [Hint: Use cot 450° = 0]
Solution:
Using trigonometry formulas,
(cos (450°) cosec (225°) sec (225°))/2 = cos (450°)/(2 sin (225°) cos (225°))
Using sin 2a formula,
2 sin (225°) cos (225°) = sin (2 × 225°) = sin 450°
⇒ cos (450°) / sin (450°) = cot 450°
⇒ (cos (450°) cosec (225°) sec (225°))/2 = 0 
Example 2: Find the value of cot 450° using sin 450° and cos 450°.
Solution:
Since, cot 450° = cos 450°/sin 450°
⇒ cot 450° = 0/1 = 0 
Example 3: Find the value of 3 cot(450°)/5 cot(45°).
Solution:
Using trigonometric identities, we know, cot(450°) = 0 and cot(45°) = 1.
⇒ Value of 3 cot(450°)/5 cot(45°) = 0
FAQs on Cot 450 Degrees
What is Cot 450 Degrees?
Cot 450 degrees is the value of cotangent trigonometric function for an angle equal to 450 degrees. The value of cot 450° is 0.
How to Find Cot 450° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cot 450° can be given in terms of other trigonometric functions as:
 cos(450°)/sin(450°)
 ± cos 450°/√(1  cos²(450°))
 ± √(1  sin²(450°))/sin 450°
 ± 1/√(sec²(450°)  1)
 ± √(cosec²(450°)  1)
 1/tan 450°
☛ Also check: trigonometry table
What is the Value of Cot 450 Degrees in Terms of Tan 450°?
Since the cotangent function is the reciprocal of the tangent function, we can write cot 450° as 1/tan(450°).
How to Find the Value of Cot 450 Degrees?
The value of cot 450 degrees can be calculated by constructing an angle of 450° with the xaxis, and then finding the coordinates of the corresponding point (0, 1) on the unit circle. The value of cot 450° is equal to the xcoordinate(0) divided by the ycoordinate (1). ∴ cot 450° = 0
What is the Value of Cot 450° in Terms of Sec 450°?
We can represent the cotangent function in terms of the secant function using trig identities, cot 450° can be written as 1/√(sec²(450°)  1).
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