Sin 8 Degrees
The value of sin 8 degrees is 0.1391731. . .. Sin 8 degrees in radians is written as sin (8° × π/180°), i.e., sin (2π/45) or sin (0.139626. . .). In this article, we will discuss the methods to find the value of sin 8 degrees with examples.
- Sin 8°: 0.1391731. . .
- Sin (-8 degrees): -0.1391731. . .
- Sin 8° in radians: sin (2π/45) or sin (0.1396263 . . .)
What is the Value of Sin 8 Degrees?
The value of sin 8 degrees in decimal is 0.139173100. . .. Sin 8 degrees can also be expressed using the equivalent of the given angle (8 degrees) in radians (0.13962 . . .).
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 8 degrees = 8° × (π/180°) rad = 2π/45 or 0.1396 . . .
∴ sin 8° = sin(0.1396) = 0.1391731. . .
Explanation:
For sin 8 degrees, the angle 8° lies between 0° and 90° (First Quadrant). Since sine function is positive in the first quadrant, thus sin 8° value = 0.1391731. . .
Since the sine function is a periodic function, we can represent sin 8° as, sin 8 degrees = sin(8° + n × 360°), n ∈ Z.
⇒ sin 8° = sin 368° = sin 728°, and so on.
Note: Since, sine is an odd function, the value of sin(-8°) = -sin(8°).
Methods to Find Value of Sin 8 Degrees
The sine function is positive in the 1st quadrant. The value of sin 8° is given as 0.13917. . .. We can find the value of sin 8 degrees by:
- Using Trigonometric Functions
- Using Unit Circle
Sin 8° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the sin 8 degrees as:
- ± √(1-cos²(8°))
- ± tan 8°/√(1 + tan²(8°))
- ± 1/√(1 + cot²(8°))
- ± √(sec²(8°) - 1)/sec 8°
- 1/cosec 8°
Note: Since 8° lies in the 1st Quadrant, the final value of sin 8° will be positive.
We can use trigonometric identities to represent sin 8° as,
- sin(180° - 8°) = sin 172°
- -sin(180° + 8°) = -sin 188°
- cos(90° - 8°) = cos 82°
- -cos(90° + 8°) = -cos 98°
Sin 8 Degrees Using Unit Circle
To find the value of sin 8 degrees using the unit circle:
- Rotate ‘r’ anticlockwise to form a 8° angle with the positive x-axis.
- The sin of 8 degrees equals the y-coordinate(0.1392) of the point of intersection (0.9903, 0.1392) of unit circle and r.
Hence the value of sin 8° = y = 0.1392 (approx)
☛ Also Check:
FAQs on Sin 8 Degrees
What is Sin 8 Degrees?
Sin 8 degrees is the value of sine trigonometric function for an angle equal to 8 degrees. The value of sin 8° is 0.1392 (approx).
What is the Value of Sin 8 Degrees in Terms of Tan 8°?
We know, using trig identities, we can write sin 8° as tan 8°/√(1 + tan²(8°)). Here, the value of tan 8° is equal to 0.140540.
What is the Exact Value of sin 8 Degrees?
The exact value of sin 8 degrees can be given accurately up to 8 decimal places as 0.13917310.
How to Find the Value of Sin 8 Degrees?
The value of sin 8 degrees can be calculated by constructing an angle of 8° with the x-axis, and then finding the coordinates of the corresponding point (0.9903, 0.1392) on the unit circle. The value of sin 8° is equal to the y-coordinate (0.1392). ∴ sin 8° = 0.1392.
How to Find Sin 8° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of sin 8° can be given in terms of other trigonometric functions as:
- ± √(1-cos²(8°))
- ± tan 8°/√(1 + tan²(8°))
- ± 1/√(1 + cot²(8°))
- ± √(sec²(8°) - 1)/sec 8°
- 1/cosec 8°
☛ Also check: trigonometry table