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 x-axis.
- The sin of 11pi/6 equals the y-coordinate(-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:
- ± √(1-cos²(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:
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 x-axis, 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 y-coordinate (-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:
- ± √(1-cos²(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.