Cot 300 Degrees
The value of cot 300 degrees is -0.5773502. . .. Cot 300 degrees in radians is written as cot (300° × π/180°), i.e., cot (5π/3) or cot (5.235987. . .). In this article, we will discuss the methods to find the value of cot 300 degrees with examples.
- Cot 300°: -(1/√3)
- Cot 300° in decimal: -0.5773502. . .
- Cot (-300 degrees): 0.5773502. . . or 1/√3
- Cot 300° in radians: cot (5π/3) or cot (5.2359877 . . .)
What is the Value of Cot 300 Degrees?
The value of cot 300 degrees in decimal is -0.577350269. . .. Cot 300 degrees can also be expressed using the equivalent of the given angle (300 degrees) in radians (5.23598 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 300 degrees = 300° × (π/180°) rad = 5π/3 or 5.2359 . . .
∴ cot 300° = cot(5.2359) = -(1/√3) or -0.5773502. . .
Explanation:
For cot 300 degrees, the angle 300° lies between 270° and 360° (Fourth Quadrant). Since cotangent function is negative in the fourth quadrant, thus cot 300° value = -(1/√3) or -0.5773502. . .
Since the cotangent function is a periodic function, we can represent cot 300° as, cot 300 degrees = cot(300° + n × 180°), n ∈ Z.
⇒ cot 300° = cot 480° = cot 660°, and so on.
Note: Since, cotangent is an odd function, the value of cot(-300°) = -cot(300°).
Methods to Find Value of Cot 300 Degrees
The cotangent function is negative in the 4th quadrant. The value of cot 300° is given as -0.57735. . . We can find the value of cot 300 degrees by:
- Using Trigonometric Functions
- Using Unit Circle
Cot 300° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cot 300 degrees as:
- cos(300°)/sin(300°)
- ± cos 300°/√(1 - cos²(300°))
- ± √(1 - sin²(300°))/sin 300°
- ± 1/√(sec²(300°) - 1)
- ± √(cosec²(300°) - 1)
- 1/tan 300°
Note: Since 300° lies in the 4th Quadrant, the final value of cot 300° will be negative.
We can use trigonometric identities to represent cot 300° as,
- tan (90° - 300°) = tan(-210°)
- -tan (90° + 300°) = -tan 390°
- -cot (180° - 300°) = -cot(-120°)
Cot 300 Degrees Using Unit Circle
To find the value of cot 300 degrees using the unit circle:
- Rotate ‘r’ anticlockwise to form 300° angle with the positive x-axis.
- The cot of 300 degrees equals the x-coordinate(0.5) divided by y-coordinate(-0.866) of the point of intersection (0.5, -0.866) of unit circle and r.
Hence the value of cot 300° = x/y = -0.5774 (approx).
☛ Also Check:
FAQs on Cot 300 Degrees
What is Cot 300 Degrees?
Cot 300 degrees is the value of cotangent trigonometric function for an angle equal to 300 degrees. The value of cot 300° is -(1/√3) or -0.5774 (approx).
What is the Value of Cot 300 Degrees in Terms of Sin 300°?
Using trigonometric identities, we can write cot 300° in terms of sin 300° as, cot(300°) = √(1 - sin²(300°))/sin 300° . Here, the value of sin 300° is equal to -(√3/2).
How to Find Cot 300° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cot 300° can be given in terms of other trigonometric functions as:
- cos(300°)/sin(300°)
- ± cos 300°/√(1 - cos²(300°))
- ± √(1 - sin²(300°))/sin 300°
- ± 1/√(sec²(300°) - 1)
- ± √(cosec²(300°) - 1)
- 1/tan 300°
☛ Also check: trigonometry table
How to Find the Value of Cot 300 Degrees?
The value of cot 300 degrees can be calculated by constructing an angle of 300° with the x-axis, and then finding the coordinates of the corresponding point (0.5, -0.866) on the unit circle. The value of cot 300° is equal to the x-coordinate(0.5) divided by the y-coordinate (-0.866). ∴ cot 300° = -0.5774
What is the Value of Cot 300° in Terms of Cosec 300°?
Since the cotangent function can be represented using the cosecant function, we can write cot 300° as -√(cosec²(300°) - 1). The value of cosec 300° is equal to -1.15470.