Sin 12 Degrees

The value of sin 12 degrees is 0.2079116. . .. Sin 12 degrees in radians is written as sin (12° × π/180°), i.e., sin (π/15) or sin (0.209439. . .). In this article, we will discuss the methods to find the value of sin 12 degrees with examples.

• Sin 12°: 0.2079116. . .
• Sin (-12 degrees): -0.2079116. . .
• Sin 12° in radians: sin (π/15) or sin (0.2094395 . . .)

What is the Value of Sin 12 Degrees?

The value of sin 12 degrees in decimal is 0.207911690. . .. Sin 12 degrees can also be expressed using the equivalent of the given angle (12 degrees) in radians (0.20943 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 12 degrees = 12° × (π/180°) rad = π/15 or 0.2094 . . .
∴ sin 12° = sin(0.2094) = 0.2079116. . .

Explanation:

For sin 12 degrees, the angle 12° lies between 0° and 90° (First Quadrant). Since sine function is positive in the first quadrant, thus sin 12° value = 0.2079116. . .
Since the sine function is a periodic function, we can represent sin 12° as, sin 12 degrees = sin(12° + n × 360°), n ∈ Z.
⇒ sin 12° = sin 372° = sin 732°, and so on.
Note: Since, sine is an odd function, the value of sin(-12°) = -sin(12°).

Methods to Find Value of Sin 12 Degrees

The sine function is positive in the 1st quadrant. The value of sin 12° is given as 0.20791. . .. We can find the value of sin 12 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Sin 12 Degrees Using Unit Circle

To find the value of sin 12 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form a 12° angle with the positive x-axis.
• The sin of 12 degrees equals the y-coordinate(0.2079) of the point of intersection (0.9781, 0.2079) of unit circle and r.

Hence the value of sin 12° = y = 0.2079 (approx)

Sin 12° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 12 degrees as:

• ± √(1-cos²(12°))
• ± tan 12°/√(1 + tan²(12°))
• ± 1/√(1 + cot²(12°))
• ± √(sec²(12°) - 1)/sec 12°
• 1/cosec 12°

Note: Since 12° lies in the 1st Quadrant, the final value of sin 12° will be positive.

We can use trigonometric identities to represent sin 12° as,

• sin(180° - 12°) = sin 168°
• -sin(180° + 12°) = -sin 192°
• cos(90° - 12°) = cos 78°
• -cos(90° + 12°) = -cos 102°

☛ Also Check:

• sin 36 degrees
• sin 50 degrees
• sin 90 degrees
• sin 210 degrees
• sin 660 degrees
• sin 1000 degrees

FAQs on Sin 12 Degrees

What is Sin 12 Degrees?

Sin 12 degrees is the value of sine trigonometric function for an angle equal to 12 degrees. The value of sin 12° is 0.2079 (approx).

How to Find Sin 12° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 12° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(12°))
• ± tan 12°/√(1 + tan²(12°))
• ± 1/√(1 + cot²(12°))
• ± √(sec²(12°) - 1)/sec 12°
• 1/cosec 12°

☛ Also check: trigonometry table

What is the Value of Sin 12 Degrees in Terms of Tan 12°?

We know, using trig identities, we can write sin 12° as tan 12°/√(1 + tan²(12°)). Here, the value of tan 12° is equal to 0.212556.

What is the Value of Sin 12° in Terms of Cosec 12°?

Since the cosecant function is the reciprocal of the sine function, we can write sin 12° as 1/cosec(12°). The value of cosec 12° is equal to 4.80973.

How to Find the Value of Sin 12 Degrees?

The value of sin 12 degrees can be calculated by constructing an angle of 12° with the x-axis, and then finding the coordinates of the corresponding point (0.9781, 0.2079) on the unit circle. The value of sin 12° is equal to the y-coordinate (0.2079). ∴ sin 12° = 0.2079.