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Sin 11pi/6
The value of sin 11pi/6 is 0.5. Sin 11pi/6 radians in degrees is written as sin ((11π/6) × 180°/π), i.e., sin (330°). In this article, we will discuss the methods to find the value of sin 11pi/6 with examples.
 Sin 11pi/6: (1/2)
 Sin 11pi/6 in decimal: 0.5
 Sin (11pi/6): 0.5 or 1/2
 Sin 11pi/6 in degrees: sin (330°)
What is the Value of Sin 11pi/6?
The value of sin 11pi/6 in decimal is 0.5. Sin 11pi/6 can also be expressed using the equivalent of the given angle (11pi/6) in degrees (330°).
We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)
⇒ 11pi/6 radians = 11pi/6 × (180°/pi) = 330° or 330 degrees
∴ sin 11pi/6 = sin 11π/6 = sin(330°) = (1/2) or 0.5
Explanation:
For sin 11pi/6, the angle 11pi/6 lies between 3pi/2 and 2pi (Fourth Quadrant). Since sine function is negative in the fourth quadrant, thus sin 11pi/6 value = (1/2) or 0.5
Since the sine function is a periodic function, we can represent sin 11pi/6 as, sin 11pi/6 = sin(11pi/6 + n × 2pi), n ∈ Z.
⇒ sin 11pi/6 = sin 23pi/6 = sin 35pi/6 , and so on.
Note: Since, sine is an odd function, the value of sin(11pi/6) = sin(11pi/6).
Methods to Find Value of Sin 11pi/6
The sine function is negative in the 4th quadrant. The value of sin 11pi/6 is given as 0.5. We can find the value of sin 11pi/6 by:
 Using Unit Circle
 Using Trigonometric Functions
Sin 11pi/6 Using Unit Circle
To find the value of sin 11π/6 using the unit circle:
 Rotate ‘r’ anticlockwise to form 11pi/6 angle with the positive xaxis.
 The sin of 11pi/6 equals the ycoordinate(0.5) of the point of intersection (0.866, 0.5) of unit circle and r.
Hence the value of sin 11pi/6 = y = 0.5
Sin 11pi/6 in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the sin 11pi/6 as:
 ± √(1cos²(11pi/6))
 ± tan(11pi/6)/√(1 + tan²(11pi/6))
 ± 1/√(1 + cot²(11pi/6))
 ± √(sec²(11pi/6)  1)/sec(11pi/6)
 1/cosec(11pi/6)
Note: Since 11pi/6 lies in the 4th Quadrant, the final value of sin 11pi/6 will be negative.
We can use trigonometric identities to represent sin 11pi/6 as,
 sin(pi  11pi/6) = sin(5pi/6)
 sin(pi + 11pi/6) = sin 17pi/6
 cos(pi/2  11pi/6) = cos(4pi/3)
 cos(pi/2 + 11pi/6) = cos 7pi/3
☛ Also Check:
Examples Using Sin 11pi/6

Example 1: Using the value of sin 11pi/6, solve: (1cos²(11pi/6)).
Solution:
We know, (1cos²(11pi/6)) = (sin²(11pi/6)) = 0.25
⇒ (1cos²(11pi/6)) = 0.25 
Example 2: Simplify: 2 (sin(11pi/6)/sin(23pi/6))
Solution:
We know sin 11pi/6 = sin 23pi/6
⇒ 2 sin(11pi/6)/sin(23pi/6) = 2(sin(11pi/6)/sin(11pi/6))
= 2(1) = 2 
Example 3: Find the value of 5 sin(11pi/6)/7 cos(4pi/3).
Solution:
Using trigonometric identities, we know, sin(11pi/6) = cos(pi/2  11pi/6) = cos(4pi/3).
⇒ sin(11pi/6) = cos(4pi/3)
⇒ Value of 5 sin(11pi/6)/7 cos(4pi/3) = 5/7
FAQs on Sin 11pi/6
What is Sin 11pi/6?
Sin 11pi/6 is the value of sine trigonometric function for an angle equal to 11pi/6 radians. The value of sin 11pi/6 is (1/2) or 0.5.
How to Find the Value of Sin 11pi/6?
The value of sin 11pi/6 can be calculated by constructing an angle of 11π/6 radians with the xaxis, and then finding the coordinates of the corresponding point (0.866, 0.5) on the unit circle. The value of sin 11pi/6 is equal to the ycoordinate (0.5). ∴ sin 11pi/6 = 0.5.
What is the Value of Sin 11pi/6 in Terms of Cot 11pi/6?
We can represent the sine function in terms of the cotangent function using trig identities, sin 11pi/6 can be written as 1/√(1 + cot²(11pi/6)). Here, the value of cot 11pi/6 is equal to 1.7321.
How to Find Sin 11pi/6 in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of sin 11π/6 can be given in terms of other trigonometric functions as:
 ± √(1cos²(11pi/6))
 ± tan(11pi/6)/√(1 + tan²(11pi/6))
 ± 1/√(1 + cot²(11pi/6))
 ± √(sec²(11pi/6)  1)/sec(11pi/6)
 1/cosec(11pi/6)
☛ Also check: trigonometry table
What is the Value of Sin 11pi/6 in Terms of Cosec 11pi/6?
Since the cosecant function is the reciprocal of the sine function, we can write sin 11pi/6 as 1/cosec(11pi/6). The value of cosec 11pi/6 is equal to 2.
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