0.2588190 is the value of sin 15 degrees. In radians, sin 15 degrees is expressed as sin (15° /180°), i.e., sin (12). (0.261799. . .).
With examples, we’ll go over how to get the value of sin 15 degrees in this article.
- 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 decimal equivalent of sin 15 degrees is 0.258819045. The equivalent of the given angle (15 degrees) in radians may likewise be used to represent Sin 15 degrees (0.26179 . . .).
Using the degree to radian conversion, we know that in radians Equals 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:
The angle 15° is between 0° and 90° for sin 15 degrees (First Quadrant). Because the sine function is positive in the first quadrant, the value of sin 15° is (6 – 2)/4 or 0.2588190.
The sine function is a periodic function, therefore it’s easy to remember.
, 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°).
Sin 15° in Terms of Trigonometric Functions
The sin 15 degrees can be written as follows using trigonometry formulas:
- ± √(1-cos²(15°))
- ± tan 15°/√(1 + tan²(15°))
- ± 1/√(1 + cot²(15°))
- ± √(sec²(15°) – 1)/sec 15°
- 1/cosec 15°
Note: Because 15° is in the first quadrant, sin 15° will have a positive final value.
To represent sin 15°, we may utilise trigonometric identities such,
- sin(180° – 15°) = sin 165°
- -sin(180° + 15°) = -sin 195°
- cos(90° – 15°) = cos 75°
- -cos(90° + 15°) = -cos 105°
