Cot 570 Degrees
The value of cot 570 degrees is 1.7320508. . .. Cot 570 degrees in radians is written as cot (570° × π/180°), i.e., cot (19π/6) or cot (9.948376. . .). In this article, we will discuss the methods to find the value of cot 570 degrees with examples.
- Cot 570°: √3
- Cot 570° in decimal: 1.7320508. . .
- Cot (-570 degrees): -1.7320508. . . or -√3
- Cot 570° in radians: cot (19π/6) or cot (9.9483767 . . .)
What is the Value of Cot 570 Degrees?
The value of cot 570 degrees in decimal is 1.732050807. . .. Cot 570 degrees can also be expressed using the equivalent of the given angle (570 degrees) in radians (9.94837 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 570 degrees = 570° × (π/180°) rad = 19π/6 or 9.9483 . . .
∴ cot 570° = cot(9.9483) = √3 or 1.7320508. . .
Explanation:
For cot 570°, the angle 570° > 360°. We can represent cot 570° as, cot(570° mod 360°) = cot(210°). The angle 570°, coterminal to angle 210°, is located in the Third Quadrant(Quadrant III).
Since cotangent function is positive in the 3rd quadrant, thus cot 570 degrees value = √3 or 1.7320508. . .
Similarly, given the periodic property of cot 570°, it can also be written as, cot 570 degrees = (570° + n × 180°), n ∈ Z.
⇒ cot 570° = cot 750° = cot 930°, and so on.
Note: Since, cotangent is an odd function, the value of cot(-570°) = -cot(570°).
Methods to Find Value of Cot 570 Degrees
The cotangent function is positive in the 3rd quadrant. The value of cot 570° is given as 1.73205. . . We can find the value of cot 570 degrees by:
- Using Unit Circle
- Using Trigonometric Functions
Cot 570 Degrees Using Unit Circle
To find the value of cot 570 degrees using the unit circle, represent 570° in the form (1 × 360°) + 210° [∵ 570°>360°] ∵ The angle 570° is coterminal to 210° angle and also cotangent is a periodic function, cot 570° = cot 210°.
- Rotate ‘r’ anticlockwise to form 210° or 570° angle with the positive x-axis.
- The cot of 570 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 570° = x/y = 1.7321 (approx).
Cot 570° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cot 570 degrees as:
- cos(570°)/sin(570°)
- ± cos 570°/√(1 - cos²(570°))
- ± √(1 - sin²(570°))/sin 570°
- ± 1/√(sec²(570°) - 1)
- ± √(cosec²(570°) - 1)
- 1/tan 570°
Note: Since 570° lies in the 3rd Quadrant, the final value of cot 570° will be positive.
We can use trigonometric identities to represent cot 570° as,
- tan (90° - 570°) = tan(-480°)
- -tan (90° + 570°) = -tan 660°
- -cot (180° - 570°) = -cot(-390°)
☛ Also Check:
FAQs on Cot 570 Degrees
What is Cot 570 Degrees?
Cot 570 degrees is the value of cotangent trigonometric function for an angle equal to 570 degrees. The value of cot 570° is √3 or 1.7321 (approx).
What is the Value of Cot 570° in Terms of Cosec 570°?
Since the cotangent function can be represented using the cosecant function, we can write cot 570° as √(cosec²(570°) - 1). The value of cosec 570° is equal to -2.
How to Find the Value of Cot 570 Degrees?
The value of cot 570 degrees can be calculated by constructing an angle of 570° 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 570° is equal to the x-coordinate(-0.866) divided by the y-coordinate (-0.5). ∴ cot 570° = 1.7321
What is the Value of Cot 570 Degrees in Terms of Cos 570°?
We know, using trig identities, we can write cot 570° as -cos 570°/√(1 - cos²(570°)). Here, the value of cos 570° is equal to -0.866025.
How to Find Cot 570° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cot 570° can be given in terms of other trigonometric functions as:
- cos(570°)/sin(570°)
- ± cos 570°/√(1 - cos²(570°))
- ± √(1 - sin²(570°))/sin 570°
- ± 1/√(sec²(570°) - 1)
- ± √(cosec²(570°) - 1)
- 1/tan 570°
☛ Also check: trigonometric table