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:

• ± √(1-cos²(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 x-axis.
• The sin of 2 degrees equals the y-coordinate(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:

• sin 13 degrees
• sin 150 degrees
• sin 3 degrees
• sin 28 degrees
• sin 17 degrees
• sin 105 degrees

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 x-axis, 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 y-coordinate (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:

• ± √(1-cos²(2°))
• ± tan 2°/√(1 + tan²(2°))
• ± 1/√(1 + cot²(2°))
• ± √(sec²(2°) - 1)/sec 2°
• 1/cosec 2°

☛ Also check: trigonometry table