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Sin 56 Degrees
The value of sin 56 degrees is 0.8290375. . .. Sin 56 degrees in radians is written as sin (56° × π/180°), i.e., sin (14π/45) or sin (0.977384. . .). In this article, we will discuss the methods to find the value of sin 56 degrees with examples.
 Sin 56°: 0.8290375. . .
 Sin (56 degrees): 0.8290375. . .
 Sin 56° in radians: sin (14π/45) or sin (0.9773843 . . .)
What is the Value of Sin 56 Degrees?
The value of sin 56 degrees in decimal is 0.829037572. . .. Sin 56 degrees can also be expressed using the equivalent of the given angle (56 degrees) in radians (0.97738 . . .).
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 56 degrees = 56° × (π/180°) rad = 14π/45 or 0.9773 . . .
∴ sin 56° = sin(0.9773) = 0.8290375. . .
Explanation:
For sin 56 degrees, the angle 56° lies between 0° and 90° (First Quadrant). Since sine function is positive in the first quadrant, thus sin 56° value = 0.8290375. . .
Since the sine function is a periodic function, we can represent sin 56° as, sin 56 degrees = sin(56° + n × 360°), n ∈ Z.
⇒ sin 56° = sin 416° = sin 776°, and so on.
Note: Since, sine is an odd function, the value of sin(56°) = sin(56°).
Methods to Find Value of Sin 56 Degrees
The sine function is positive in the 1st quadrant. The value of sin 56° is given as 0.82903. . .. We can find the value of sin 56 degrees by:
 Using Trigonometric Functions
 Using Unit Circle
Sin 56° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the sin 56 degrees as:
 ± √(1cos²(56°))
 ± tan 56°/√(1 + tan²(56°))
 ± 1/√(1 + cot²(56°))
 ± √(sec²(56°)  1)/sec 56°
 1/cosec 56°
Note: Since 56° lies in the 1st Quadrant, the final value of sin 56° will be positive.
We can use trigonometric identities to represent sin 56° as,
 sin(180°  56°) = sin 124°
 sin(180° + 56°) = sin 236°
 cos(90°  56°) = cos 34°
 cos(90° + 56°) = cos 146°
Sin 56 Degrees Using Unit Circle
To find the value of sin 56 degrees using the unit circle:
 Rotate ‘r’ anticlockwise to form a 56° angle with the positive xaxis.
 The sin of 56 degrees equals the ycoordinate(0.829) of the point of intersection (0.5592, 0.829) of unit circle and r.
Hence the value of sin 56° = y = 0.829 (approx)
☛ Also Check:
Examples Using Sin 56 Degrees

Example 1: Find the value of 5 sin(56°)/7 cos(34°).
Solution:
Using trigonometric identities, we know, sin(56°) = cos(90°  56°) = cos 34°.
⇒ sin(56°) = cos(34°)
⇒ Value of 5 sin(56°)/7 cos(34°) = 5/7 
Example 2: Find the value of 2 × (sin 28° cos 28°). [Hint: Use sin 56° = 0.829]
Solution:
Using the sin 2a formula,
2 sin 28° cos 28° = sin(2 × 28°) = sin 56°
∵ sin 56° = 0.829
⇒ 2 × (sin 28° cos 28°) = 0.829 
Example 3: Find the value of sin 56° if cosec 56° is 1.2062.
Solution:
Since, sin 56° = 1/csc 56°
⇒ sin 56° = 1/1.2062 = 0.829
FAQs on Sin 56 Degrees
What is Sin 56 Degrees?
Sin 56 degrees is the value of sine trigonometric function for an angle equal to 56 degrees. The value of sin 56° is 0.829 (approx).
What is the Value of Sin 56 Degrees in Terms of Tan 56°?
We know, using trig identities, we can write sin 56° as tan 56°/√(1 + tan²(56°)). Here, the value of tan 56° is equal to 1.482560.
How to Find Sin 56° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of sin 56° can be given in terms of other trigonometric functions as:
 ± √(1cos²(56°))
 ± tan 56°/√(1 + tan²(56°))
 ± 1/√(1 + cot²(56°))
 ± √(sec²(56°)  1)/sec 56°
 1/cosec 56°
☛ Also check: trigonometry table
What is the Exact Value of sin 56 Degrees?
The exact value of sin 56 degrees can be given accurately up to 8 decimal places as 0.82903757.
How to Find the Value of Sin 56 Degrees?
The value of sin 56 degrees can be calculated by constructing an angle of 56° with the xaxis, and then finding the coordinates of the corresponding point (0.5592, 0.829) on the unit circle. The value of sin 56° is equal to the ycoordinate (0.829). ∴ sin 56° = 0.829.
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