Sin 15 Degrees

The value of sin 15 degrees is 0.2588190. . .. Sin 15 degrees in radians is written as sin (15° × π/180°), i.e., sin (π/12) or sin (0.261799. . .). In this article, we will discuss the methods to find the value of sin 15 degrees with examples.

• Sin 15°: 0.2588190. . .
• Sin 15° in fraction: (√6 - √2)/4
• Sin (-15 degrees): -0.2588190. . .
• Sin 15° in radians: sin (π/12) or sin (0.2617993 . . .)

What is the Value of Sin 15 Degrees?

The value of sin 15 degrees in decimal is 0.258819045. . .. Sin 15 degrees can also be expressed using the equivalent of the given angle (15 degrees) in radians (0.26179 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 15 degrees = 15° × (π/180°) rad = π/12 or 0.2617 . . .
∴ sin 15° = sin(0.2617) = (√6 - √2)/4 or 0.2588190. . .

Explanation:

For sin 15 degrees, the angle 15° lies between 0° and 90° (First Quadrant). Since sine function is positive in the first quadrant, thus sin 15° value = (√6 - √2)/4 or 0.2588190. . .
Since the sine function is a periodic function, we can represent sin 15° as, sin 15 degrees = sin(15° + n × 360°), n ∈ Z.
⇒ sin 15° = sin 375° = sin 735°, and so on.
Note: Since, sine is an odd function, the value of sin(-15°) = -sin(15°).

Methods to Find Value of Sin 15 Degrees

The sine function is positive in the 1st quadrant. The value of sin 15° is given as 0.25881. . .. We can find the value of sin 15 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Sin 15 Degrees Using Unit Circle

To find the value of sin 15 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form a 15° angle with the positive x-axis.
• The sin of 15 degrees 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 15° = y = 0.2588 (approx)

Sin 15° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 15 degrees as:

• ± √(1-cos²(15°))
• ± tan 15°/√(1 + tan²(15°))
• ± 1/√(1 + cot²(15°))
• ± √(sec²(15°) - 1)/sec 15°
• 1/cosec 15°

Note: Since 15° lies in the 1st Quadrant, the final value of sin 15° will be positive.

We can use trigonometric identities to represent sin 15° as,

• sin(180° - 15°) = sin 165°
• -sin(180° + 15°) = -sin 195°
• cos(90° - 15°) = cos 75°
• -cos(90° + 15°) = -cos 105°

☛ Also Check:

• sin 2 degrees
• sin 45 degrees
• sin 0 degrees
• sin 95 degrees
• sin 48 degrees
• sin 933 degrees

FAQs on Sin 15 Degrees

What is Sin 15 Degrees?

Sin 15 degrees is the value of sine trigonometric function for an angle equal to 15 degrees. The value of sin 15° is (√6 - √2)/4 or 0.2588 (approx).

What is the Value of Sin 15 Degrees in Terms of Tan 15°?

We know, using trig identities, we can write sin 15° as tan 15°/√(1 + tan²(15°)). Here, the value of tan 15° is equal to 0.267949.

How to Find Sin 15° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 15° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(15°))
• ± tan 15°/√(1 + tan²(15°))
• ± 1/√(1 + cot²(15°))
• ± √(sec²(15°) - 1)/sec 15°
• 1/cosec 15°

☛ Also check: trigonometric table

How to Find the Value of Sin 15 Degrees?

The value of sin 15 degrees can be calculated by constructing an angle of 15° 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 15° is equal to the y-coordinate (0.2588). ∴ sin 15° = 0.2588.

What is the Value of Sin 15° in Terms of Sec 15°?

Since the sine function can be represented using the secant function, we can write sin 15° as √(sec²(15°) - 1)/sec 15°. The value of sec 15° is equal to 1.035276.