Sin 6 Degrees

The value of sin 6 degrees is 0.1045284. . .. Sin 6 degrees in radians is written as sin (6° × π/180°), i.e., sin (π/30) or sin (0.104719. . .). In this article, we will discuss the methods to find the value of sin 6 degrees with examples.

• Sin 6°: 0.1045284. . .
• Sin (-6 degrees): -0.1045284. . .
• Sin 6° in radians: sin (π/30) or sin (0.1047197 . . .)

What is the Value of Sin 6 Degrees?

The value of sin 6 degrees in decimal is 0.104528463. . .. Sin 6 degrees can also be expressed using the equivalent of the given angle (6 degrees) in radians (0.10471 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 6 degrees = 6° × (π/180°) rad = π/30 or 0.1047 . . .
∴ sin 6° = sin(0.1047) = 0.1045284. . .

Explanation:

For sin 6 degrees, the angle 6° lies between 0° and 90° (First Quadrant). Since sine function is positive in the first quadrant, thus sin 6° value = 0.1045284. . .
Since the sine function is a periodic function, we can represent sin 6° as, sin 6 degrees = sin(6° + n × 360°), n ∈ Z.
⇒ sin 6° = sin 366° = sin 726°, and so on.
Note: Since, sine is an odd function, the value of sin(-6°) = -sin(6°).

Methods to Find Value of Sin 6 Degrees

The sine function is positive in the 1st quadrant. The value of sin 6° is given as 0.10452. . .. We can find the value of sin 6 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Sin 6° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 6 degrees as:

• ± √(1-cos²(6°))
• ± tan 6°/√(1 + tan²(6°))
• ± 1/√(1 + cot²(6°))
• ± √(sec²(6°) - 1)/sec 6°
• 1/cosec 6°

Note: Since 6° lies in the 1st Quadrant, the final value of sin 6° will be positive.

We can use trigonometric identities to represent sin 6° as,

• sin(180° - 6°) = sin 174°
• -sin(180° + 6°) = -sin 186°
• cos(90° - 6°) = cos 84°
• -cos(90° + 6°) = -cos 96°

Sin 6 Degrees Using Unit Circle

To find the value of sin 6 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form a 6° angle with the positive x-axis.
• The sin of 6 degrees equals the y-coordinate(0.1045) of the point of intersection (0.9945, 0.1045) of unit circle and r.

Hence the value of sin 6° = y = 0.1045 (approx)

☛ Also Check:

• sin 30 degrees
• sin 60 degrees
• sin 11 degrees
• sin 14 degrees
• sin 960 degrees
• sin 83 degrees

FAQs on Sin 6 Degrees

What is Sin 6 Degrees?

Sin 6 degrees is the value of sine trigonometric function for an angle equal to 6 degrees. The value of sin 6° is 0.1045 (approx).

How to Find the Value of Sin 6 Degrees?

The value of sin 6 degrees can be calculated by constructing an angle of 6° with the x-axis, and then finding the coordinates of the corresponding point (0.9945, 0.1045) on the unit circle. The value of sin 6° is equal to the y-coordinate (0.1045). ∴ sin 6° = 0.1045.

How to Find Sin 6° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 6° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(6°))
• ± tan 6°/√(1 + tan²(6°))
• ± 1/√(1 + cot²(6°))
• ± √(sec²(6°) - 1)/sec 6°
• 1/cosec 6°

☛ Also check: trigonometric table

What is the Exact Value of sin 6 Degrees?

The exact value of sin 6 degrees can be given accurately up to 8 decimal places as 0.10452846.

What is the Value of Sin 6 Degrees in Terms of Cos 6°?

Using trigonometric identities, we can write sin 6° in terms of cos 6° as, sin(6°) = √(1-cos²(6°)). Here, the value of cos 6° is equal to 0.9945218.