Cot 53 Degrees

The value of cot 53 degrees is 0.7535540. . .. Cot 53 degrees in radians is written as cot (53° × π/180°), i.e., cot (0.925024. . .). In this article, we will discuss the methods to find the value of cot 53 degrees with examples.

• Cot 53° in decimal: 0.7535540. . .
• Cot (-53 degrees): -0.7535540. . .
• Cot 53° in radians: cot (0.9250245 . . .)

What is the Value of Cot 53 Degrees?

The value of cot 53 degrees in decimal is 0.753554050. . .. Cot 53 degrees can also be expressed using the equivalent of the given angle (53 degrees) in radians (0.92502 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 53 degrees = 53° × (π/180°) rad = 0.9250 . . .
∴ cot 53° = cot(0.9250) = 0.7535540. . .

Explanation:

For cot 53 degrees, the angle 53° lies between 0° and 90° (First Quadrant). Since cotangent function is positive in the first quadrant, thus cot 53° value = 0.7535540. . .
Since the cotangent function is a periodic function, we can represent cot 53° as, cot 53 degrees = cot(53° + n × 180°), n ∈ Z.
⇒ cot 53° = cot 233° = cot 413°, and so on.
Note: Since, cotangent is an odd function, the value of cot(-53°) = -cot(53°).

Methods to Find Value of Cot 53 Degrees

The cotangent function is positive in the 1st quadrant. The value of cot 53° is given as 0.75355. . . We can find the value of cot 53 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Cot 53 Degrees Using Unit Circle

To find the value of cot 53 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 53° angle with the positive x-axis.
• The cot of 53 degrees equals the x-coordinate(0.6018) divided by y-coordinate(0.7986) of the point of intersection (0.6018, 0.7986) of unit circle and r.

Hence the value of cot 53° = x/y = 0.7536 (approx).

Cot 53° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cot 53 degrees as:

• cos(53°)/sin(53°)
• ± cos 53°/√(1 - cos²(53°))
• ± √(1 - sin²(53°))/sin 53°
• ± 1/√(sec²(53°) - 1)
• ± √(cosec²(53°) - 1)
• 1/tan 53°

Note: Since 53° lies in the 1st Quadrant, the final value of cot 53° will be positive.

We can use trigonometric identities to represent cot 53° as,

• tan (90° - 53°) = tan 37°
• -tan (90° + 53°) = -tan 143°
• -cot (180° - 53°) = -cot 127°

☛ Also Check:

• cot 150 degrees
• cot 70 degrees
• cot 10 degrees
• cot 34 degrees
• cot 60 degrees
• cot 3 degrees

FAQs on Cot 53 Degrees

What is Cot 53 Degrees?

Cot 53 degrees is the value of cotangent trigonometric function for an angle equal to 53 degrees. The value of cot 53° is 0.7536 (approx).

What is the Value of Cot 53° in Terms of Cosec 53°?

Since the cotangent function can be represented using the cosecant function, we can write cot 53° as √(cosec²(53°) - 1). The value of cosec 53° is equal to 1.25213.

How to Find Cot 53° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cot 53° can be given in terms of other trigonometric functions as:

• cos(53°)/sin(53°)
• ± cos 53°/√(1 - cos²(53°))
• ± √(1 - sin²(53°))/sin 53°
• ± 1/√(sec²(53°) - 1)
• ± √(cosec²(53°) - 1)
• 1/tan 53°

☛ Also check: trigonometric table

How to Find the Value of Cot 53 Degrees?

The value of cot 53 degrees can be calculated by constructing an angle of 53° with the x-axis, and then finding the coordinates of the corresponding point (0.6018, 0.7986) on the unit circle. The value of cot 53° is equal to the x-coordinate(0.6018) divided by the y-coordinate (0.7986). ∴ cot 53° = 0.7536

What is the Value of Cot 53 Degrees in Terms of Cos 53°?

We know, using trig identities, we can write cot 53° as cos 53°/√(1 - cos²(53°)). Here, the value of cos 53° is equal to 0.601815.