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:

• ± √(1-cos²(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 x-axis.
• The sin of pi/12 equals the y-coordinate(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:

• cos pi/6
• tan 7pi/8
• sec 3pi
• sin 7pi
• cos 2pi
• sin 2pi

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:

• ± √(1-cos²(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) = √(1-cos²(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 x-axis, 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 y-coordinate (0.2588). ∴ sin pi/12 = 0.2588.