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 y-axis.
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 x-axis.
• The cot of 450 degrees equals the x-coordinate(0) divided by y-coordinate(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 y-axis, 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:

• cot 11 degrees
• cot 600 degrees
• cot 15 degrees
• cot 225 degrees
• cot 360 degrees
• cot 20 degrees

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 x-axis, and then finding the coordinates of the corresponding point (0, 1) on the unit circle. The value of cot 450° is equal to the x-coordinate(0) divided by the y-coordinate (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).