Tan 570 Degrees
The value of tan 570 degrees is 0.5773502. . .. Tan 570 degrees in radians is written as tan (570° × π/180°), i.e., tan (19π/6) or tan (9.948376. . .). In this article, we will discuss the methods to find the value of tan 570 degrees with examples.
- Tan 570°: 1/√3
- Tan 570° in decimal: 0.5773502. . .
- Tan (-570 degrees): -0.5773502. . . or -1/√3
- Tan 570° in radians: tan (19π/6) or tan (9.9483767 . . .)
What is the Value of Tan 570 Degrees?
The value of tan 570 degrees in decimal is 0.577350269. . .. Tan 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 . . .
∴ tan 570° = tan(9.9483) = 1/√3 or 0.5773502. . .
Explanation:
For tan 570°, the angle 570° > 360°. We can represent tan 570° as, tan(570° mod 360°) = tan(210°). The angle 570°, coterminal to angle 210°, is located in the Third Quadrant(Quadrant III).
Since tangent function is positive in the 3rd quadrant, thus tan 570 degrees value = 1/√3 or 0.5773502. . .
Similarly, given the periodic property of tan 570°, it can also be written as, tan 570 degrees = (570° + n × 180°), n ∈ Z.
⇒ tan 570° = tan 750° = tan 930°, and so on.
Note: Since, tangent is an odd function, the value of tan(-570°) = -tan(570°).
Methods to Find Value of Tan 570 Degrees
The tangent function is positive in the 3rd quadrant. The value of tan 570° is given as 0.57735. . .. We can find the value of tan 570 degrees by:
- Using Unit Circle
- Using Trigonometric Functions
Tan 570 Degrees Using Unit Circle
To find the value of tan 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 tangent is a periodic function, tan 570° = tan 210°.
- Rotate ‘r’ anticlockwise to form 210° or 570° angle with the positive x-axis.
- The tan of 570 degrees equals the y-coordinate(-0.5) divided by x-coordinate(-0.866) of the point of intersection (-0.866, -0.5) of unit circle and r.
Hence the value of tan 570° = y/x = 0.5774 (approx).
Tan 570° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the tan 570 degrees as:
- sin(570°)/cos(570°)
- ± sin 570°/√(1 - sin²(570°))
- ± √(1 - cos²(570°))/cos 570°
- ± 1/√(cosec²(570°) - 1)
- ± √(sec²(570°) - 1)
- 1/cot 570°
Note: Since 570° lies in the 3rd Quadrant, the final value of tan 570° will be positive.
We can use trigonometric identities to represent tan 570° as,
- cot(90° - 570°) = cot(-480°)
- -cot(90° + 570°) = -cot 660°
- -tan (180° - 570°) = -tan(-390°)
☛ Also Check:
FAQs on Tan 570 Degrees
What is Tan 570 Degrees?
Tan 570 degrees is the value of tangent trigonometric function for an angle equal to 570 degrees. The value of tan 570° is 1/√3 or 0.5774 (approx).
How to Find the Value of Tan 570 Degrees?
The value of tan 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 tan 570° is equal to the y-coordinate(-0.5) divided by the x-coordinate (-0.866). ∴ tan 570° = 1/√3 or 0.5774
What is the Value of Tan 570 Degrees in Terms of Cos 570°?
We know, using trig identities, we can write tan 570° as -√(1 - cos²(570°))/cos 570°. Here, the value of cos 570° is equal to -0.866025.
How to Find Tan 570° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of tan 570° can be given in terms of other trigonometric functions as:
- sin(570°)/cos(570°)
- ± sin 570°/√(1 - sin²(570°))
- ± √(1 - cos²(570°))/cos 570°
- ± 1/√(cosec²(570°) - 1)
- ± √(sec²(570°) - 1)
- 1/cot 570°
☛ Also check: trigonometry table
What is the Value of Tan 570° in Terms of Cosec 570°?
Since the tangent function can be represented using the cosecant function, we can write tan 570° as 1/√(cosec²(570°) - 1). The value of cosec 570° is equal to -2.