Sin 556 Degrees
The value of sin 556 degrees is -0.2756373. . .. Sin 556 degrees in radians is written as sin (556° × π/180°), i.e., sin (139π/45) or sin (9.704030. . .). In this article, we will discuss the methods to find the value of sin 556 degrees with examples.
- Sin 556°: -0.2756373. . .
- Sin (-556 degrees): 0.2756373. . .
- Sin 556° in radians: sin (139π/45) or sin (9.7040306 . . .)
What is the Value of Sin 556 Degrees?
The value of sin 556 degrees in decimal is -0.275637355. . .. Sin 556 degrees can also be expressed using the equivalent of the given angle (556 degrees) in radians (9.70403 . . .).
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 556 degrees = 556° × (π/180°) rad = 139π/45 or 9.7040 . . .
∴ sin 556° = sin(9.7040) = -0.2756373. . .
Explanation:
For sin 556°, the angle 556° > 360°. Given the periodic property of the sine function, we can represent it as sin(556° mod 360°) = sin(196°). The angle 556°, coterminal to angle 196°, is located in the Third Quadrant(Quadrant III).
Since sine function is negative in the 3rd quadrant, thus sin 556 degrees value = -0.2756373. . .
Similarly, sin 556° can also be written as, sin 556 degrees = (556° + n × 360°), n ∈ Z.
⇒ sin 556° = sin 916° = sin 1276°, and so on.
Note: Since, sine is an odd function, the value of sin(-556°) = -sin(556°).
Methods to Find Value of Sin 556 Degrees
The sine function is negative in the 3rd quadrant. The value of sin 556° is given as -0.27563. . .. We can find the value of sin 556 degrees by:
- Using Trigonometric Functions
- Using Unit Circle
Sin 556° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the sin 556 degrees as:
- ± √(1-cos²(556°))
- ± tan 556°/√(1 + tan²(556°))
- ± 1/√(1 + cot²(556°))
- ± √(sec²(556°) - 1)/sec 556°
- 1/cosec 556°
Note: Since 556° lies in the 3rd Quadrant, the final value of sin 556° will be negative.
We can use trigonometric identities to represent sin 556° as,
- sin(180° - 556°) = sin(-376°)
- -sin(180° + 556°) = -sin 736°
- cos(90° - 556°) = cos(-466°)
- -cos(90° + 556°) = -cos 646°
Sin 556 Degrees Using Unit Circle
To find the value of sin 556 degrees using the unit circle, represent 556° in the form (1 × 360°) + 196° [∵ 556°>360°] ∵ sine is a periodic function, sin 556° = sin 196°.
- Rotate ‘r’ anticlockwise to form a 196° or 556° angle with the positive x-axis.
- The sin of 556 degrees equals the y-coordinate(-0.2756) of the point of intersection (-0.9613, -0.2756) of unit circle and r.
Hence the value of sin 556° = y = -0.2756 (approx)
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FAQs on Sin 556 Degrees
What is Sin 556 Degrees?
Sin 556 degrees is the value of sine trigonometric function for an angle equal to 556 degrees. The value of sin 556° is -0.2756 (approx).
What is the Value of Sin 556 Degrees in Terms of Cos 556°?
Using trigonometric identities, we can write sin 556° in terms of cos 556° as, sin(556°) = -√(1-cos²(556°)). Here, the value of cos 556° is equal to -0.9612616.
What is the Value of Sin 556° in Terms of Cosec 556°?
Since the cosecant function is the reciprocal of the sine function, we can write sin 556° as 1/cosec(556°). The value of cosec 556° is equal to -3.62795.
How to Find the Value of Sin 556 Degrees?
The value of sin 556 degrees can be calculated by constructing an angle of 556° with the x-axis, and then finding the coordinates of the corresponding point (-0.9613, -0.2756) on the unit circle. The value of sin 556° is equal to the y-coordinate (-0.2756). ∴ sin 556° = -0.2756.
How to Find Sin 556° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of sin 556° can be given in terms of other trigonometric functions as:
- ± √(1-cos²(556°))
- ± tan 556°/√(1 + tan²(556°))
- ± 1/√(1 + cot²(556°))
- ± √(sec²(556°) - 1)/sec 556°
- 1/cosec 556°
☛ Also check: trigonometry table