Cot 116 Degrees

The value of cot 116 degrees is -0.4877325. . .. Cot 116 degrees in radians is written as cot (116° × π/180°), i.e., cot (29π/45) or cot (2.024581. . .). In this article, we will discuss the methods to find the value of cot 116 degrees with examples.

• Cot 116° in decimal: -0.4877325. . .
• Cot (-116 degrees): 0.4877325. . .
• Cot 116° in radians: cot (29π/45) or cot (2.0245819 . . .)

What is the Value of Cot 116 Degrees?

The value of cot 116 degrees in decimal is -0.487732588. . .. Cot 116 degrees can also be expressed using the equivalent of the given angle (116 degrees) in radians (2.02458 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 116 degrees = 116° × (π/180°) rad = 29π/45 or 2.0245 . . .
∴ cot 116° = cot(2.0245) = -0.4877325. . .

Explanation:

For cot 116 degrees, the angle 116° lies between 90° and 180° (Second Quadrant). Since cotangent function is negative in the second quadrant, thus cot 116° value = -0.4877325. . .
Since the cotangent function is a periodic function, we can represent cot 116° as, cot 116 degrees = cot(116° + n × 180°), n ∈ Z.
⇒ cot 116° = cot 296° = cot 476°, and so on.
Note: Since, cotangent is an odd function, the value of cot(-116°) = -cot(116°).

Methods to Find Value of Cot 116 Degrees

The cotangent function is negative in the 2nd quadrant. The value of cot 116° is given as -0.48773. . . We can find the value of cot 116 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Cot 116 Degrees Using Unit Circle

To find the value of cot 116 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 116° angle with the positive x-axis.
• The cot of 116 degrees equals the x-coordinate(-0.4384) divided by y-coordinate(0.8988) of the point of intersection (-0.4384, 0.8988) of unit circle and r.

Hence the value of cot 116° = x/y = -0.4877 (approx).

Cot 116° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cot 116 degrees as:

• cos(116°)/sin(116°)
• ± cos 116°/√(1 - cos²(116°))
• ± √(1 - sin²(116°))/sin 116°
• ± 1/√(sec²(116°) - 1)
• ± √(cosec²(116°) - 1)
• 1/tan 116°

Note: Since 116° lies in the 2nd Quadrant, the final value of cot 116° will be negative.

We can use trigonometric identities to represent cot 116° as,

• tan (90° - 116°) = tan(-26°)
• -tan (90° + 116°) = -tan 206°
• -cot (180° - 116°) = -cot 64°

☛ Also Check:

• cot 37 degrees
• cot 120 degrees
• cot 11 degrees
• cot 60 degrees
• cot 18 degrees
• cot 55 degrees

FAQs on Cot 116 Degrees

What is Cot 116 Degrees?

Cot 116 degrees is the value of cotangent trigonometric function for an angle equal to 116 degrees. The value of cot 116° is -0.4877 (approx).

How to Find the Value of Cot 116 Degrees?

The value of cot 116 degrees can be calculated by constructing an angle of 116° with the x-axis, and then finding the coordinates of the corresponding point (-0.4384, 0.8988) on the unit circle. The value of cot 116° is equal to the x-coordinate(-0.4384) divided by the y-coordinate (0.8988). ∴ cot 116° = -0.4877

What is the Value of Cot 116 Degrees in Terms of Cos 116°?

We know, using trig identities, we can write cot 116° as cos 116°/√(1 - cos²(116°)). Here, the value of cos 116° is equal to -0.438371.

What is the Exact Value of Cot 116 Degrees?

The exact value of cot 116 degrees can be given accurately up to 8 decimal places as -0.48773258.

How to Find Cot 116° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cot 116° can be given in terms of other trigonometric functions as:

• cos(116°)/sin(116°)
• ± cos 116°/√(1 - cos²(116°))
• ± √(1 - sin²(116°))/sin 116°
• ± 1/√(sec²(116°) - 1)
• ± √(cosec²(116°) - 1)
• 1/tan 116°

☛ Also check: trigonometry table