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 talk about the methods to discover the value of sin pi/6 with examples.

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Sin pi/6: 1/2Sin pi/6 in decimal: 0.5Sin (-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 additionally be expressed making use of the equivalent of the provided angle (pi/6) in levels (30°).

We know, using radian to level conversion, θ in levels = 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). Due to the fact that sine function is positive in the very first quadrant, thus sin pi/6 worth = 1/2 or 0.5Since 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 one odd function, the worth of sin(-pi/6) = -sin(pi/6).

## Methods to uncover Value the Sin pi/6

The sine role is positive in the first quadrant. The value of sin pi/6 is provided as 0.5. We can find the value of sin pi/6 by:

Using Trigonometric FunctionsUsing Unit Circle

## Sin pi/6 in regards to 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: because pi/6 lies in the first Quadrant, the final value the sin pi/6 will certainly be positive.

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We deserve to use trigonometric identities to stand for sin pi/6 as,

sin(pi - pi/6) = sin 5pi/6-sin(pi + pi/6) = -sin 7pi/6cos(pi/2 - pi/6) = cos pi/3-cos(pi/2 + pi/6) = -cos 2pi/3

## Sin pi/6 utilizing Unit Circle

To find the worth of sin π/6 making use of the unit circle:

Rotate ‘r’ anticlockwise to kind pi/6 angle with the confident x-axis.The sin the pi/6 amounts to the y-coordinate(0.5) that the point of intersection (0.866, 0.5) that unit circle and also r.

Hence the value of sin pi/6 = y = 0.5