Cos 570 Degrees
The value of cos 570 degrees is -0.8660254. . .. Cos 570 degrees in radians is written as cos (570° × π/180°), i.e., cos (19π/6) or cos (9.948376. . .). In this article, we will discuss the methods to find the value of cos 570 degrees with examples.
- Cos 570°: -0.8660254. . .
- Cos 570° in fraction: -√(3)/2
- Cos (-570 degrees): -0.8660254. . .
- Cos 570° in radians: cos (19π/6) or cos (9.9483767 . . .)
What is the Value of Cos 570 Degrees?
The value of cos 570 degrees in decimal is -0.866025403. . .. Cos 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 . . .
∴ cos 570° = cos(9.9483) = -√(3)/2 or -0.8660254. . .
Explanation:
For cos 570°, the angle 570° > 360°. Given the periodic property of the cosine function, we can represent it as cos(570° mod 360°) = cos(210°). The angle 570°, coterminal to angle 210°, is located in the Third Quadrant(Quadrant III).
Since cosine function is negative in the 3rd quadrant, thus cos 570 degrees value = -√(3)/2 or -0.8660254. . .
Similarly, cos 570° can also be written as, cos 570 degrees = (570° + n × 360°), n ∈ Z.
⇒ cos 570° = cos 930° = cos 1290°, and so on.
Note: Since, cosine is an even function, the value of cos(-570°) = cos(570°).
Methods to Find Value of Cos 570 Degrees
The cosine function is negative in the 3rd quadrant. The value of cos 570° is given as -0.86602. . .. We can find the value of cos 570 degrees by:
- Using Trigonometric Functions
- Using Unit Circle
Cos 570° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cos 570 degrees as:
- ± √(1-sin²(570°))
- ± 1/√(1 + tan²(570°))
- ± cot 570°/√(1 + cot²(570°))
- ±√(cosec²(570°) - 1)/cosec 570°
- 1/sec 570°
Note: Since 570° lies in the 3rd Quadrant, the final value of cos 570° will be negative.
We can use trigonometric identities to represent cos 570° as,
- -cos(180° - 570°) = -cos(-390°)
- -cos(180° + 570°) = -cos 750°
- sin(90° + 570°) = sin 660°
- sin(90° - 570°) = sin(-480°)
Cos 570 Degrees Using Unit Circle
To find the value of cos 570 degrees using the unit circle, represent 570° in the form (1 × 360°) + 210° [∵ 570°>360°] ∵ cosine is a periodic function, cos 570° = cos 210°.
- Rotate ‘r’ anticlockwise to form 210° or 570° angle with the positive x-axis.
- The cos of 570 degrees equals the x-coordinate(-0.866) of the point of intersection (-0.866, -0.5) of unit circle and r.
Hence the value of cos 570° = x = -0.866 (approx)
☛ Also Check:
FAQs on Cos 570 Degrees
What is Cos 570 Degrees?
Cos 570 degrees is the value of cosine trigonometric function for an angle equal to 570 degrees. The value of cos 570° is -√(3)/2 or -0.866 (approx)
How to Find the Value of Cos 570 Degrees?
The value of cos 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 cos 570° is equal to the x-coordinate (-0.866). ∴ cos 570° = -0.866.
How to Find Cos 570° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cos 570° can be given in terms of other trigonometric functions as:
- ± √(1-sin²(570°))
- ± 1/√(1 + tan²(570°))
- ± cot 570°/√(1 + cot²(570°))
- ± √(cosec²(570°) - 1)/cosec 570°
- 1/sec 570°
☛ Also check: trigonometry table
What is the Value of Cos 570 Degrees in Terms of Tan 570°?
We know, using trig identities, we can write cos 570° as -1/√(1 + tan²(570°)). Here, the value of tan 570° is equal to 0.577350.
What is the Value of Cos 570° in Terms of Cosec 570°?
Since the cosine function can be represented using the cosecant function, we can write cos 570° as [√(cosec²(570°) - 1)/cosec 570°]. The value of cosec 570° is equal to -2.