Sin pi/6
The value of sin pi/6 is 0.5. Sin pi/6 radians in degrees is written as sin ((π/6) × 180°/π), i.e., sin (30°). In this article, we will discuss the methods to find the value of sin pi/6 with examples.
- Sin pi/6: 1/2
- Sin pi/6 in decimal: 0.5
- Sin (-pi/6): -0.5 or -(1/2)
- Sin pi/6 in degrees: sin (30°)
What is the Value of Sin pi/6?
The value of sin pi/6 in decimal is 0.5. Sin pi/6 can also be expressed using the equivalent of the given angle (pi/6) in degrees (30°).
We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)
⇒ pi/6 radians = pi/6 × (180°/pi) = 30° or 30 degrees
∴ sin pi/6 = sin π/6 = sin(30°) = 1/2 or 0.5
Explanation:
For sin pi/6, the angle pi/6 lies between 0 and pi/2 (First Quadrant). Since sine function is positive in the first quadrant, thus sin pi/6 value = 1/2 or 0.5
Since the sine function is a periodic function, we can represent sin pi/6 as, sin pi/6 = sin(pi/6 + n × 2pi), n ∈ Z.
⇒ sin pi/6 = sin 13pi/6 = sin 25pi/6 , and so on.
Note: Since, sine is an odd function, the value of sin(-pi/6) = -sin(pi/6).
Methods to Find Value of Sin pi/6
The sine function is positive in the 1st quadrant. The value of sin pi/6 is given as 0.5. We can find the value of sin pi/6 by:
- Using Trigonometric Functions
- Using Unit Circle
Sin pi/6 in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the sin pi/6 as:
- ± √(1-cos²(pi/6))
- ± tan(pi/6)/√(1 + tan²(pi/6))
- ± 1/√(1 + cot²(pi/6))
- ± √(sec²(pi/6) - 1)/sec(pi/6)
- 1/cosec(pi/6)
Note: Since pi/6 lies in the 1st Quadrant, the final value of sin pi/6 will be positive.
We can use trigonometric identities to represent sin pi/6 as,
- sin(pi - pi/6) = sin 5pi/6
- -sin(pi + pi/6) = -sin 7pi/6
- cos(pi/2 - pi/6) = cos pi/3
- -cos(pi/2 + pi/6) = -cos 2pi/3
Sin pi/6 Using Unit Circle
To find the value of sin π/6 using the unit circle:
- Rotate ‘r’ anticlockwise to form pi/6 angle with the positive x-axis.
- The sin of pi/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 pi/6 = y = 0.5
☛ Also Check:
FAQs on Sin pi/6
What is Sin pi/6?
Sin pi/6 is the value of sine trigonometric function for an angle equal to pi/6 radians. The value of sin pi/6 is 1/2 or 0.5.
What is the Value of Sin pi/6 in Terms of Cosec pi/6?
Since the cosecant function is the reciprocal of the sine function, we can write sin pi/6 as 1/cosec(pi/6). The value of cosec pi/6 is equal to 2.
How to Find the Value of Sin pi/6?
The value of sin pi/6 can be calculated by constructing an angle of π/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 pi/6 is equal to the y-coordinate (0.5). ∴ sin pi/6 = 0.5.
What is the Value of Sin pi/6 in Terms of Cot pi/6?
We can represent the sine function in terms of the cotangent function using trig identities, sin pi/6 can be written as 1/√(1 + cot²(pi/6)). Here, the value of cot pi/6 is equal to 1.7321.
How to Find Sin pi/6 in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of sin π/6 can be given in terms of other trigonometric functions as:
- ± √(1-cos²(pi/6))
- ± tan(pi/6)/√(1 + tan²(pi/6))
- ± 1/√(1 + cot²(pi/6))
- ± √(sec²(pi/6) - 1)/sec(pi/6)
- 1/cosec(pi/6)
☛ Also check: trigonometric table