Sin 11pi/12
The value of sin 11pi/12 is 0.2588190. . .. Sin 11pi/12 radians in degrees is written as sin ((11π/12) × 180°/π), i.e., sin (165°). In this article, we will discuss the methods to find the value of sin 11pi/12 with examples.
- Sin 11pi/12: (√6 - √2)/4
- Sin 11pi/12 in decimal: 0.2588190. . .
- Sin (-11pi/12): -0.2588190. . . or -(√6 - √2)/4
- Sin 11pi/12 in degrees: sin (165°)
What is the Value of Sin 11pi/12?
The value of sin 11pi/12 in decimal is 0.258819045. . .. Sin 11pi/12 can also be expressed using the equivalent of the given angle (11pi/12) in degrees (165°).
We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)
⇒ 11pi/12 radians = 11pi/12 × (180°/pi) = 165° or 165 degrees
∴ sin 11pi/12 = sin 11π/12 = sin(165°) = (√6 - √2)/4 or 0.2588190. . .
Explanation:
For sin 11pi/12, the angle 11pi/12 lies between pi/2 and pi (Second Quadrant). Since sine function is positive in the second quadrant, thus sin 11pi/12 value = (√6 - √2)/4 or 0.2588190. . .
Since the sine function is a periodic function, we can represent sin 11pi/12 as, sin 11pi/12 = sin(11pi/12 + n × 2pi), n ∈ Z.
⇒ sin 11pi/12 = sin 35pi/12 = sin 59pi/12 , and so on.
Note: Since, sine is an odd function, the value of sin(-11pi/12) = -sin(11pi/12).
Methods to Find Value of Sin 11pi/12
The sine function is positive in the 2nd quadrant. The value of sin 11pi/12 is given as 0.25881. . .. We can find the value of sin 11pi/12 by:
- Using Trigonometric Functions
- Using Unit Circle
Sin 11pi/12 in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the sin 11pi/12 as:
- ± √(1-cos²(11pi/12))
- ± tan(11pi/12)/√(1 + tan²(11pi/12))
- ± 1/√(1 + cot²(11pi/12))
- ± √(sec²(11pi/12) - 1)/sec(11pi/12)
- 1/cosec(11pi/12)
Note: Since 11pi/12 lies in the 2nd Quadrant, the final value of sin 11pi/12 will be positive.
We can use trigonometric identities to represent sin 11pi/12 as,
- sin(pi - 11pi/12) = sin pi/12
- -sin(pi + 11pi/12) = -sin 23pi/12
- cos(pi/2 - 11pi/12) = cos(-5pi/12)
- -cos(pi/2 + 11pi/12) = -cos 17pi/12
Sin 11pi/12 Using Unit Circle
To find the value of sin 11π/12 using the unit circle:
- Rotate ‘r’ anticlockwise to form 11pi/12 angle with the positive x-axis.
- The sin of 11pi/12 equals the y-coordinate(0.2588) of the point of intersection (-0.9659, 0.2588) of unit circle and r.
Hence the value of sin 11pi/12 = y = 0.2588 (approx)
☛ Also Check:
FAQs on Sin 11pi/12
What is Sin 11pi/12?
Sin 11pi/12 is the value of sine trigonometric function for an angle equal to 11pi/12 radians. The value of sin 11pi/12 is (√6 - √2)/4 or 0.2588 (approx).
What is the Value of Sin 11pi/12 in Terms of Sec 11pi/12?
Since the sine function can be represented using the secant function, we can write sin 11pi/12 as -√(sec²(11pi/12) - 1)/sec 11pi/12. The value of sec 11pi/12 is equal to -1.035276.
What is the Value of Sin 11pi/12 in Terms of Cot 11pi/12?
We can represent the sine function in terms of the cotangent function using trig identities, sin 11pi/12 can be written as 1/√(1 + cot²(11pi/12)). Here, the value of cot 11pi/12 is equal to -3.7321.
How to Find the Value of Sin 11pi/12?
The value of sin 11pi/12 can be calculated by constructing an angle of 11π/12 radians with the x-axis, and then finding the coordinates of the corresponding point (-0.9659, 0.2588) on the unit circle. The value of sin 11pi/12 is equal to the y-coordinate (0.2588). ∴ sin 11pi/12 = 0.2588.
How to Find Sin 11pi/12 in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of sin 11π/12 can be given in terms of other trigonometric functions as:
- ± √(1-cos²(11pi/12))
- ± tan(11pi/12)/√(1 + tan²(11pi/12))
- ± 1/√(1 + cot²(11pi/12))
- ± √(sec²(11pi/12) - 1)/sec(11pi/12)
- 1/cosec(11pi/12)
☛ Also check: trigonometric table