Sin 857 Degrees
The value of sin 857 degrees is 0.6819983. . .. Sin 857 degrees in radians is written as sin (857° × π/180°), i.e., sin (14.957471. . .). In this article, we will discuss the methods to find the value of sin 857 degrees with examples.
- Sin 857°: 0.6819983. . .
- Sin (-857 degrees): -0.6819983. . .
- Sin 857° in radians: sin (14.9574716 . . .)
What is the Value of Sin 857 Degrees?
The value of sin 857 degrees in decimal is 0.681998360. . .. Sin 857 degrees can also be expressed using the equivalent of the given angle (857 degrees) in radians (14.95747 . . .).
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 857 degrees = 857° × (π/180°) rad = 14.9574 . . .
∴ sin 857° = sin(14.9574) = 0.6819983. . .
Explanation:
For sin 857°, the angle 857° > 360°. Given the periodic property of the sine function, we can represent it as sin(857° mod 360°) = sin(137°). The angle 857°, coterminal to angle 137°, is located in the Second Quadrant(Quadrant II).
Since sine function is positive in the 2nd quadrant, thus sin 857 degrees value = 0.6819983. . .
Similarly, sin 857° can also be written as, sin 857 degrees = (857° + n × 360°), n ∈ Z.
⇒ sin 857° = sin 1217° = sin 1577°, and so on.
Note: Since, sine is an odd function, the value of sin(-857°) = -sin(857°).
Methods to Find Value of Sin 857 Degrees
The sine function is positive in the 2nd quadrant. The value of sin 857° is given as 0.68199. . .. We can find the value of sin 857 degrees by:
- Using Unit Circle
- Using Trigonometric Functions
Sin 857 Degrees Using Unit Circle
To find the value of sin 857 degrees using the unit circle, represent 857° in the form (2 × 360°) + 137° [∵ 857°>360°] ∵ sine is a periodic function, sin 857° = sin 137°.
- Rotate ‘r’ anticlockwise to form a 137° or 857° angle with the positive x-axis.
- The sin of 857 degrees equals the y-coordinate(0.682) of the point of intersection (-0.7314, 0.682) of unit circle and r.
Hence the value of sin 857° = y = 0.682 (approx)
Sin 857° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the sin 857 degrees as:
- ± √(1-cos²(857°))
- ± tan 857°/√(1 + tan²(857°))
- ± 1/√(1 + cot²(857°))
- ± √(sec²(857°) - 1)/sec 857°
- 1/cosec 857°
Note: Since 857° lies in the 2nd Quadrant, the final value of sin 857° will be positive.
We can use trigonometric identities to represent sin 857° as,
- sin(180° - 857°) = sin(-677°)
- -sin(180° + 857°) = -sin 1037°
- cos(90° - 857°) = cos(-767°)
- -cos(90° + 857°) = -cos 947°
☛ Also Check:
FAQs on Sin 857 Degrees
What is Sin 857 Degrees?
Sin 857 degrees is the value of sine trigonometric function for an angle equal to 857 degrees. The value of sin 857° is 0.682 (approx).
What is the Value of Sin 857 Degrees in Terms of Cos 857°?
Using trigonometric identities, we can write sin 857° in terms of cos 857° as, sin(857°) = √(1-cos²(857°)). Here, the value of cos 857° is equal to -0.7313537.
How to Find Sin 857° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of sin 857° can be given in terms of other trigonometric functions as:
- ± √(1-cos²(857°))
- ± tan 857°/√(1 + tan²(857°))
- ± 1/√(1 + cot²(857°))
- ± √(sec²(857°) - 1)/sec 857°
- 1/cosec 857°
☛ Also check: trigonometric table
How to Find the Value of Sin 857 Degrees?
The value of sin 857 degrees can be calculated by constructing an angle of 857° with the x-axis, and then finding the coordinates of the corresponding point (-0.7314, 0.682) on the unit circle. The value of sin 857° is equal to the y-coordinate (0.682). ∴ sin 857° = 0.682.
What is the Value of Sin 857° in Terms of Sec 857°?
Since the sine function can be represented using the secant function, we can write sin 857° as -√(sec²(857°) - 1)/sec 857°. The value of sec 857° is equal to -1.367327.