Cot 600 Degrees
The value of cot 600 degrees is 0.5773502. . .. Cot 600 degrees in radians is written as cot (600° × π/180°), i.e., cot (10π/3) or cot (10.471975. . .). In this article, we will discuss the methods to find the value of cot 600 degrees with examples.
- Cot 600°: 1/√3
- Cot 600° in decimal: 0.5773502. . .
- Cot (-600 degrees): -0.5773502. . . or -(1/√3)
- Cot 600° in radians: cot (10π/3) or cot (10.4719755 . . .)
What is the Value of Cot 600 Degrees?
The value of cot 600 degrees in decimal is 0.577350269. . .. Cot 600 degrees can also be expressed using the equivalent of the given angle (600 degrees) in radians (10.47197 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 600 degrees = 600° × (π/180°) rad = 10π/3 or 10.4719 . . .
∴ cot 600° = cot(10.4719) = 1/√3 or 0.5773502. . .
Explanation:
For cot 600°, the angle 600° > 360°. We can represent cot 600° as, cot(600° mod 360°) = cot(240°). The angle 600°, coterminal to angle 240°, is located in the Third Quadrant(Quadrant III).
Since cotangent function is positive in the 3rd quadrant, thus cot 600 degrees value = 1/√3 or 0.5773502. . .
Similarly, given the periodic property of cot 600°, it can also be written as, cot 600 degrees = (600° + n × 180°), n ∈ Z.
⇒ cot 600° = cot 780° = cot 960°, and so on.
Note: Since, cotangent is an odd function, the value of cot(-600°) = -cot(600°).
Methods to Find Value of Cot 600 Degrees
The cotangent function is positive in the 3rd quadrant. The value of cot 600° is given as 0.57735. . . We can find the value of cot 600 degrees by:
- Using Trigonometric Functions
- Using Unit Circle
Cot 600° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cot 600 degrees as:
- cos(600°)/sin(600°)
- ± cos 600°/√(1 - cos²(600°))
- ± √(1 - sin²(600°))/sin 600°
- ± 1/√(sec²(600°) - 1)
- ± √(cosec²(600°) - 1)
- 1/tan 600°
Note: Since 600° lies in the 3rd Quadrant, the final value of cot 600° will be positive.
We can use trigonometric identities to represent cot 600° as,
- tan (90° - 600°) = tan(-510°)
- -tan (90° + 600°) = -tan 690°
- -cot (180° - 600°) = -cot(-420°)
Cot 600 Degrees Using Unit Circle
To find the value of cot 600 degrees using the unit circle, represent 600° in the form (1 × 360°) + 240° [∵ 600°>360°] ∵ The angle 600° is coterminal to 240° angle and also cotangent is a periodic function, cot 600° = cot 240°.
- Rotate ‘r’ anticlockwise to form 240° or 600° angle with the positive x-axis.
- The cot of 600 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 600° = x/y = 0.5774 (approx).
☛ Also Check:
FAQs on Cot 600 Degrees
What is Cot 600 Degrees?
Cot 600 degrees is the value of cotangent trigonometric function for an angle equal to 600 degrees. The value of cot 600° is 1/√3 or 0.5774 (approx).
What is the Value of Cot 600° in Terms of Sec 600°?
We can represent the cotangent function in terms of the secant function using trig identities, cot 600° can be written as 1/√(sec²(600°) - 1). Here, the value of sec 600° is equal to -2.
How to Find Cot 600° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cot 600° can be given in terms of other trigonometric functions as:
- cos(600°)/sin(600°)
- ± cos 600°/√(1 - cos²(600°))
- ± √(1 - sin²(600°))/sin 600°
- ± 1/√(sec²(600°) - 1)
- ± √(cosec²(600°) - 1)
- 1/tan 600°
☛ Also check: trigonometric table
What is the Value of Cot 600 Degrees in Terms of Cos 600°?
We know, using trig identities, we can write cot 600° as -cos 600°/√(1 - cos²(600°)). Here, the value of cos 600° is equal to -0.5.
How to Find the Value of Cot 600 Degrees?
The value of cot 600 degrees can be calculated by constructing an angle of 600° 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 600° is equal to the x-coordinate(-0.5) divided by the y-coordinate (-0.866). ∴ cot 600° = 0.5774