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Sin 2 Degrees
The value of sin 2 degrees is 0.0348994. . .. Sin 2 degrees in radians is written as sin (2° × π/180°), i.e., sin (π/90) or sin (0.034906. . .). In this article, we will discuss the methods to find the value of sin 2 degrees with examples.
 Sin 2°: 0.0348994. . .
 Sin (2 degrees): 0.0348994. . .
 Sin 2° in radians: sin (π/90) or sin (0.0349065 . . .)
What is the Value of Sin 2 Degrees?
The value of sin 2 degrees in decimal is 0.034899496. . .. Sin 2 degrees can also be expressed using the equivalent of the given angle (2 degrees) in radians (0.03490 . . .).
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 2 degrees = 2° × (π/180°) rad = π/90 or 0.0349 . . .
∴ sin 2° = sin(0.0349) = 0.0348994. . .
Explanation:
For sin 2 degrees, the angle 2° lies between 0° and 90° (First Quadrant). Since sine function is positive in the first quadrant, thus sin 2° value = 0.0348994. . .
Since the sine function is a periodic function, we can represent sin 2° as, sin 2 degrees = sin(2° + n × 360°), n ∈ Z.
⇒ sin 2° = sin 362° = sin 722°, and so on.
Note: Since, sine is an odd function, the value of sin(2°) = sin(2°).
Methods to Find Value of Sin 2 Degrees
The sine function is positive in the 1st quadrant. The value of sin 2° is given as 0.03489. . .. We can find the value of sin 2 degrees by:
 Using Trigonometric Functions
 Using Unit Circle
Sin 2° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the sin 2 degrees as:
 ± √(1cos²(2°))
 ± tan 2°/√(1 + tan²(2°))
 ± 1/√(1 + cot²(2°))
 ± √(sec²(2°)  1)/sec 2°
 1/cosec 2°
Note: Since 2° lies in the 1st Quadrant, the final value of sin 2° will be positive.
We can use trigonometric identities to represent sin 2° as,
 sin(180°  2°) = sin 178°
 sin(180° + 2°) = sin 182°
 cos(90°  2°) = cos 88°
 cos(90° + 2°) = cos 92°
Sin 2 Degrees Using Unit Circle
To find the value of sin 2 degrees using the unit circle:
 Rotate ‘r’ anticlockwise to form a 2° angle with the positive xaxis.
 The sin of 2 degrees equals the ycoordinate(0.0349) of the point of intersection (0.9994, 0.0349) of unit circle and r.
Hence the value of sin 2° = y = 0.0349 (approx)
☛ Also Check:
Examples Using Sin 2 Degrees

Example 1: Find the value of 5 sin(2°)/7 cos(88°).
Solution:
Using trigonometric identities, we know, sin(2°) = cos(90°  2°) = cos 88°.
⇒ sin(2°) = cos(88°)
⇒ Value of 5 sin(2°)/7 cos(88°) = 5/7 
Example 2: Simplify: 2 (sin 2°/sin 362°)
Solution:
We know sin 2° = sin 362°
⇒ 2 sin 2°/sin 362° = 2(sin 2°/sin 2°)
= 2(1) = 2 
Example 3: Find the value of 2 × (sin 1° cos 1°). [Hint: Use sin 2° = 0.0349]
Solution:
Using the sin 2a formula,
2 sin 1° cos 1° = sin(2 × 1°) = sin 2°
∵ sin 2° = 0.0349
⇒ 2 × (sin 1° cos 1°) = 0.0349
FAQs on Sin 2 Degrees
What is Sin 2 Degrees?
Sin 2 degrees is the value of sine trigonometric function for an angle equal to 2 degrees. The value of sin 2° is 0.0349 (approx).
How to Find the Value of Sin 2 Degrees?
The value of sin 2 degrees can be calculated by constructing an angle of 2° with the xaxis, and then finding the coordinates of the corresponding point (0.9994, 0.0349) on the unit circle. The value of sin 2° is equal to the ycoordinate (0.0349). ∴ sin 2° = 0.0349.
What is the Exact Value of sin 2 Degrees?
The exact value of sin 2 degrees can be given accurately up to 8 decimal places as 0.03489949.
What is the Value of Sin 2 Degrees in Terms of Tan 2°?
We know, using trig identities, we can write sin 2° as tan 2°/√(1 + tan²(2°)). Here, the value of tan 2° is equal to 0.034920.
How to Find Sin 2° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of sin 2° can be given in terms of other trigonometric functions as:
 ± √(1cos²(2°))
 ± tan 2°/√(1 + tan²(2°))
 ± 1/√(1 + cot²(2°))
 ± √(sec²(2°)  1)/sec 2°
 1/cosec 2°
☛ Also check: trigonometry table
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