Cot 55 Degrees

The value of cot 55 degrees is 0.7002075. . .. Cot 55 degrees in radians is written as cot (55° × π/180°), i.e., cot (11π/36) or cot (0.959931. . .). In this article, we will discuss the methods to find the value of cot 55 degrees with examples.

• Cot 55° in decimal: 0.7002075. . .
• Cot (-55 degrees): -0.7002075. . .
• Cot 55° in radians: cot (11π/36) or cot (0.9599310 . . .)

What is the Value of Cot 55 Degrees?

The value of cot 55 degrees in decimal is 0.700207538. . .. Cot 55 degrees can also be expressed using the equivalent of the given angle (55 degrees) in radians (0.95993 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 55 degrees = 55° × (π/180°) rad = 11π/36 or 0.9599 . . .
∴ cot 55° = cot(0.9599) = 0.7002075. . .

Explanation:

For cot 55 degrees, the angle 55° lies between 0° and 90° (First Quadrant). Since cotangent function is positive in the first quadrant, thus cot 55° value = 0.7002075. . .
Since the cotangent function is a periodic function, we can represent cot 55° as, cot 55 degrees = cot(55° + n × 180°), n ∈ Z.
⇒ cot 55° = cot 235° = cot 415°, and so on.
Note: Since, cotangent is an odd function, the value of cot(-55°) = -cot(55°).

Methods to Find Value of Cot 55 Degrees

The cotangent function is positive in the 1st quadrant. The value of cot 55° is given as 0.70020. . . We can find the value of cot 55 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Cot 55 Degrees Using Unit Circle

To find the value of cot 55 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 55° angle with the positive x-axis.
• The cot of 55 degrees equals the x-coordinate(0.5736) divided by y-coordinate(0.8192) of the point of intersection (0.5736, 0.8192) of unit circle and r.

Hence the value of cot 55° = x/y = 0.7002 (approx).

Cot 55° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cot 55 degrees as:

• cos(55°)/sin(55°)
• ± cos 55°/√(1 - cos²(55°))
• ± √(1 - sin²(55°))/sin 55°
• ± 1/√(sec²(55°) - 1)
• ± √(cosec²(55°) - 1)
• 1/tan 55°

Note: Since 55° lies in the 1st Quadrant, the final value of cot 55° will be positive.

We can use trigonometric identities to represent cot 55° as,

• tan (90° - 55°) = tan 35°
• -tan (90° + 55°) = -tan 145°
• -cot (180° - 55°) = -cot 125°

☛ Also Check:

• cot 240 degrees
• cot 55 degrees
• cot 60 degrees
• cot 90 degrees
• cot 315 degrees
• cot 12 degrees

FAQs on Cot 55 Degrees

What is Cot 55 Degrees?

Cot 55 degrees is the value of cotangent trigonometric function for an angle equal to 55 degrees. The value of cot 55° is 0.7002 (approx).

How to Find Cot 55° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cot 55° can be given in terms of other trigonometric functions as:

• cos(55°)/sin(55°)
• ± cos 55°/√(1 - cos²(55°))
• ± √(1 - sin²(55°))/sin 55°
• ± 1/√(sec²(55°) - 1)
• ± √(cosec²(55°) - 1)
• 1/tan 55°

☛ Also check: trigonometry table

What is the Value of Cot 55° in Terms of Sec 55°?

We can represent the cotangent function in terms of the secant function using trig identities, cot 55° can be written as 1/√(sec²(55°) - 1). Here, the value of sec 55° is equal to 1.7434.

How to Find the Value of Cot 55 Degrees?

The value of cot 55 degrees can be calculated by constructing an angle of 55° with the x-axis, and then finding the coordinates of the corresponding point (0.5736, 0.8192) on the unit circle. The value of cot 55° is equal to the x-coordinate(0.5736) divided by the y-coordinate (0.8192). ∴ cot 55° = 0.7002

What is the Value of Cot 55 Degrees in Terms of Cos 55°?

We know, using trig identities, we can write cot 55° as cos 55°/√(1 - cos²(55°)). Here, the value of cos 55° is equal to 0.573576.