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Sin pi/12
The value of sin pi/12 is 0.2588190. . .. Sin pi/12 radians in degrees is written as sin ((π/12) × 180°/π), i.e., sin (15°). In this article, we will discuss the methods to find the value of sin pi/12 with examples.
 Sin pi/12: (√6  √2)/4
 Sin pi/12 in decimal: 0.2588190. . .
 Sin (pi/12): 0.2588190. . . or (√6  √2)/4
 Sin pi/12 in degrees: sin (15°)
What is the Value of Sin pi/12?
The value of sin pi/12 in decimal is 0.258819045. . .. Sin pi/12 can also be expressed using the equivalent of the given angle (pi/12) in degrees (15°).
We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)
⇒ pi/12 radians = pi/12 × (180°/pi) = 15° or 15 degrees
∴ sin pi/12 = sin π/12 = sin(15°) = (√6  √2)/4 or 0.2588190. . .
Explanation:
For sin pi/12, the angle pi/12 lies between 0 and pi/2 (First Quadrant). Since sine function is positive in the first quadrant, thus sin pi/12 value = (√6  √2)/4 or 0.2588190. . .
Since the sine function is a periodic function, we can represent sin pi/12 as, sin pi/12 = sin(pi/12 + n × 2pi), n ∈ Z.
⇒ sin pi/12 = sin 25pi/12 = sin 49pi/12 , and so on.
Note: Since, sine is an odd function, the value of sin(pi/12) = sin(pi/12).
Methods to Find Value of Sin pi/12
The sine function is positive in the 1st quadrant. The value of sin pi/12 is given as 0.25881. . .. We can find the value of sin pi/12 by:
 Using Trigonometric Functions
 Using Unit Circle
Sin pi/12 in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the sin pi/12 as:
 ± √(1cos²(pi/12))
 ± tan(pi/12)/√(1 + tan²(pi/12))
 ± 1/√(1 + cot²(pi/12))
 ± √(sec²(pi/12)  1)/sec(pi/12)
 1/cosec(pi/12)
Note: Since pi/12 lies in the 1st Quadrant, the final value of sin pi/12 will be positive.
We can use trigonometric identities to represent sin pi/12 as,
 sin(pi  pi/12) = sin 11pi/12
 sin(pi + pi/12) = sin 13pi/12
 cos(pi/2  pi/12) = cos 5pi/12
 cos(pi/2 + pi/12) = cos 7pi/12
Sin pi/12 Using Unit Circle
To find the value of sin π/12 using the unit circle:
 Rotate ‘r’ anticlockwise to form pi/12 angle with the positive xaxis.
 The sin of pi/12 equals the ycoordinate(0.2588) of the point of intersection (0.9659, 0.2588) of unit circle and r.
Hence the value of sin pi/12 = y = 0.2588 (approx)
☛ Also Check:
Examples Using Sin pi/12

Example 1: Find the value of 5 sin(pi/12)/7 cos(5pi/12).
Solution:
Using trigonometric identities, we know, sin(pi/12) = cos(pi/2  pi/12) = cos(5pi/12).
⇒ sin(pi/12) = cos(5pi/12)
⇒ Value of 5 sin(pi/12)/7 cos(5pi/12) = 5/7 
Example 2: Find the value of sin(pi/12) if cosec(pi/12) is 3.8637.
Solution:
Since, sin pi/12 = 1/csc(pi/12)
⇒ sin pi/12 = 1/3.8637 = 0.2588 
Example 3: Using the value of sin pi/12, solve: (1cos²(pi/12)).
Solution:
We know, (1cos²(pi/12)) = (sin²(pi/12)) = 0.067
⇒ (1cos²(pi/12)) = 0.067
FAQs on Sin pi/12
What is Sin pi/12?
Sin pi/12 is the value of sine trigonometric function for an angle equal to pi/12 radians. The value of sin pi/12 is (√6  √2)/4 or 0.2588 (approx).
How to Find Sin pi/12 in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of sin π/12 can be given in terms of other trigonometric functions as:
 ± √(1cos²(pi/12))
 ± tan(pi/12)/√(1 + tan²(pi/12))
 ± 1/√(1 + cot²(pi/12))
 ± √(sec²(pi/12)  1)/sec(pi/12)
 1/cosec(pi/12)
☛ Also check: trigonometry table
What is the Value of Sin pi/12 in Terms of Cosec pi/12?
Since the cosecant function is the reciprocal of the sine function, we can write sin pi/12 as 1/cosec(pi/12). The value of cosec pi/12 is equal to 3.86370.
What is the Value of Sin pi/12 in Terms of Cos pi/12?
Using trigonometric identities, we can write sin pi/12 in terms of cos pi/12 as, sin(pi/12) = √(1cos²(pi/12)). Here, the value of cos pi/12 is equal to (√6 + √2)/4.
How to Find the Value of Sin pi/12?
The value of sin pi/12 can be calculated by constructing an angle of π/12 radians with the xaxis, and then finding the coordinates of the corresponding point (0.9659, 0.2588) on the unit circle. The value of sin pi/12 is equal to the ycoordinate (0.2588). ∴ sin pi/12 = 0.2588.
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