Cot 330 Degrees

The value of cot 330 degrees is -1.7320508. . .. Cot 330 degrees in radians is written as cot (330° × π/180°), i.e., cot (11π/6) or cot (5.759586. . .). In this article, we will discuss the methods to find the value of cot 330 degrees with examples.

• Cot 330°: -√3
• Cot 330° in decimal: -1.7320508. . .
• Cot (-330 degrees): 1.7320508. . . or √3
• Cot 330° in radians: cot (11π/6) or cot (5.7595865 . . .)

What is the Value of Cot 330 Degrees?

The value of cot 330 degrees in decimal is -1.732050807. . .. Cot 330 degrees can also be expressed using the equivalent of the given angle (330 degrees) in radians (5.75958 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 330 degrees = 330° × (π/180°) rad = 11π/6 or 5.7595 . . .
∴ cot 330° = cot(5.7595) = -√3 or -1.7320508. . .

Explanation:

For cot 330 degrees, the angle 330° lies between 270° and 360° (Fourth Quadrant). Since cotangent function is negative in the fourth quadrant, thus cot 330° value = -√3 or -1.7320508. . .
Since the cotangent function is a periodic function, we can represent cot 330° as, cot 330 degrees = cot(330° + n × 180°), n ∈ Z.
⇒ cot 330° = cot 510° = cot 690°, and so on.
Note: Since, cotangent is an odd function, the value of cot(-330°) = -cot(330°).

Methods to Find Value of Cot 330 Degrees

The cotangent function is negative in the 4th quadrant. The value of cot 330° is given as -1.73205. . . We can find the value of cot 330 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Cot 330 Degrees Using Unit Circle

To find the value of cot 330 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 330° angle with the positive x-axis.
• The cot of 330 degrees equals the x-coordinate(0.866) divided by y-coordinate(-0.5) of the point of intersection (0.866, -0.5) of unit circle and r.

Hence the value of cot 330° = x/y = -1.7321 (approx).

Cot 330° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cot 330 degrees as:

• cos(330°)/sin(330°)
• ± cos 330°/√(1 - cos²(330°))
• ± √(1 - sin²(330°))/sin 330°
• ± 1/√(sec²(330°) - 1)
• ± √(cosec²(330°) - 1)
• 1/tan 330°

Note: Since 330° lies in the 4th Quadrant, the final value of cot 330° will be negative.

We can use trigonometric identities to represent cot 330° as,

• tan (90° - 330°) = tan(-240°)
• -tan (90° + 330°) = -tan 420°
• -cot (180° - 330°) = -cot(-150°)

☛ Also Check:

• cot 238 degrees
• cot 450 degrees
• cot 1 degrees
• cot 180 degrees
• cot 53 degrees
• cot 90 degrees

FAQs on Cot 330 Degrees

What is Cot 330 Degrees?

Cot 330 degrees is the value of cotangent trigonometric function for an angle equal to 330 degrees. The value of cot 330° is -√3 or -1.7321 (approx).

How to Find the Value of Cot 330 Degrees?

The value of cot 330 degrees can be calculated by constructing an angle of 330° with the x-axis, and then finding the coordinates of the corresponding point (0.866, -0.5) on the unit circle. The value of cot 330° is equal to the x-coordinate(0.866) divided by the y-coordinate (-0.5). ∴ cot 330° = -1.7321

What is the Exact Value of Cot 330 Degrees?

The exact value of cot 330 degrees can be given accurately up to 8 decimal places as -1.73205080 or as -√3.

What is the Value of Cot 330 Degrees in Terms of Sin 330°?

Using trigonometric identities, we can write cot 330° in terms of sin 330° as, cot(330°) = √(1 - sin²(330°))/sin 330° . Here, the value of sin 330° is equal to -(1/2).

How to Find Cot 330° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cot 330° can be given in terms of other trigonometric functions as:

• cos(330°)/sin(330°)
• ± cos 330°/√(1 - cos²(330°))
• ± √(1 - sin²(330°))/sin 330°
• ± 1/√(sec²(330°) - 1)
• ± √(cosec²(330°) - 1)
• 1/tan 330°

☛ Also check: trigonometry table