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:

• cot pi/8
• cot 3pi/2
• sin 5pi
• sin 5pi/4
• cot pi/2
• tan 5pi/3

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