Sin 11 Degrees

The value of sin 11 degrees is 0.1908089. . .. Sin 11 degrees in radians is written as sin (11° × π/180°), i.e., sin (0.191986. . .). In this article, we will discuss the methods to find the value of sin 11 degrees with examples.

• Sin 11°: 0.1908089. . .
• Sin (-11 degrees): -0.1908089. . .
• Sin 11° in radians: sin (0.1919862 . . .)

What is the Value of Sin 11 Degrees?

The value of sin 11 degrees in decimal is 0.190808995. . .. Sin 11 degrees can also be expressed using the equivalent of the given angle (11 degrees) in radians (0.19198 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 11 degrees = 11° × (π/180°) rad = 0.1919 . . .
∴ sin 11° = sin(0.1919) = 0.1908089. . .

Explanation:

For sin 11 degrees, the angle 11° lies between 0° and 90° (First Quadrant). Since sine function is positive in the first quadrant, thus sin 11° value = 0.1908089. . .
Since the sine function is a periodic function, we can represent sin 11° as, sin 11 degrees = sin(11° + n × 360°), n ∈ Z.
⇒ sin 11° = sin 371° = sin 731°, and so on.
Note: Since, sine is an odd function, the value of sin(-11°) = -sin(11°).

Methods to Find Value of Sin 11 Degrees

The sine function is positive in the 1st quadrant. The value of sin 11° is given as 0.19080. . .. We can find the value of sin 11 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Sin 11° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 11 degrees as:

• ± √(1-cos²(11°))
• ± tan 11°/√(1 + tan²(11°))
• ± 1/√(1 + cot²(11°))
• ± √(sec²(11°) - 1)/sec 11°
• 1/cosec 11°

Note: Since 11° lies in the 1st Quadrant, the final value of sin 11° will be positive.

We can use trigonometric identities to represent sin 11° as,

• sin(180° - 11°) = sin 169°
• -sin(180° + 11°) = -sin 191°
• cos(90° - 11°) = cos 79°
• -cos(90° + 11°) = -cos 101°

Sin 11 Degrees Using Unit Circle

To find the value of sin 11 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 11° angle with the positive x-axis.
• The sin of 11 degrees equals the y-coordinate(0.1908) of the point of intersection (0.9816, 0.1908) of unit circle and r.

Hence the value of sin 11° = y = 0.1908 (approx)

☛ Also Check:

• sin 556 degrees
• sin 60 degrees
• sin 360 degrees
• sin 83 degrees
• sin 903 degrees
• sin 315 degrees

FAQs on Sin 11 Degrees

What is Sin 11 Degrees?

Sin 11 degrees is the value of sine trigonometric function for an angle equal to 11 degrees. The value of sin 11° is 0.1908 (approx).

What is the Exact Value of sin 11 Degrees?

The exact value of sin 11 degrees can be given accurately up to 8 decimal places as 0.19080899.

How to Find Sin 11° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 11° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(11°))
• ± tan 11°/√(1 + tan²(11°))
• ± 1/√(1 + cot²(11°))
• ± √(sec²(11°) - 1)/sec 11°
• 1/cosec 11°

☛ Also check: trigonometry table

How to Find the Value of Sin 11 Degrees?

The value of sin 11 degrees can be calculated by constructing an angle of 11° with the x-axis, and then finding the coordinates of the corresponding point (0.9816, 0.1908) on the unit circle. The value of sin 11° is equal to the y-coordinate (0.1908). ∴ sin 11° = 0.1908.

What is the Value of Sin 11 Degrees in Terms of Cot 11°?

We can represent the sine function in terms of the cotangent function using trig identities, sin 11° can be written as 1/√(1 + cot²(11°)). Here, the value of cot 11° is equal to 5.14455.