The value of sin pi is 0. Sin pi radians in degrees is written as sin ((π) × 180°/π), i.e., sin (180°). In this article, we will discuss the methods to find the value of sin pi with examples.

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Sin pi: 0Sin (-pi): 0Sin pi in degrees: sin (180°)

What is the Value of Sin pi?

The value of sin pi is 0. Sin pi can also be expressed using the equivalent of the given angle (pi) in degrees (180°).

We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)⇒ pi radians = pi × (180°/pi) = 180° or 180 degrees∴ sin pi = sin π = sin(180°) = 0

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Explanation:

For sin pi, the angle pi lies on the negative x-axis. Thus, sin pi value = 0Since the sine function is a periodic function, we can represent sin pi as, sin pi = sin(pi + n × 2pi), n ∈ Z.⇒ sin pi = sin 3pi = sin 5pi , & so on.Note: Since, sine is an odd function, the value of sin(-pi) = -sin(pi) = 0.

Methods to Find Value of Sin pi

The value of sin pi is given as 0. We can find the value of sin pi by:

Using Unit CircleUsing Trigonometric Functions

Sin pi Using Unit Circle

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To find the value of sin π using the unit circle:

Rotate ‘r’ anticlockwise to khung pi angle with the positive x-axis.The sin of pi equals the y-coordinate(0) of the point of intersection (-1, 0) of unit circle và r.

Hence the value of sin pi = y = 0

Sin pi in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin pi as:

± √(1-cos²(pi))± tan(pi)/√(1 + tan²(pi))± 1/√(1 + cot²(pi))± √(sec²(pi) - 1)/sec(pi)1/cosec(pi)

Note: Since pi lies on the negative x-axis, the final value of sin pi is 0.

We can use trigonometric identities lớn represent sin pi as,

sin(pi - pi) = sin 0-sin(pi + pi) = -sin 2picos(pi/2 - pi) = cos(-pi/2)-cos(pi/2 + pi) = -cos 3pi/2

☛ Also Check:


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FAQs on Sin pi

What is Sin pi?

Sin pi is the value of sine trigonometric function for an angle equal khổng lồ pi radians. The value of sin pi is 0.

How to lớn Find Sin pi in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin π can be given in terms of other trigonometric functions as:

± √(1-cos²(pi))± tan(pi)/√(1 + tan²(pi))± 1/√(1 + cot²(pi))± √(sec²(pi) - 1)/sec(pi)1/cosec(pi)

☛ Also check: trigonometric table

How to lớn Find the Value of Sin pi?

The value of sin pi can be calculated by constructing an angle of π radians with the x-axis, và then finding the coordinates of the corresponding point (-1, 0) on the unit circle. The value of sin pi is equal to lớn the y-coordinate (0). ∴ sin pi = 0.

What is the Value of Sin pi in Terms of Cos pi?

Using trigonometric identities, we can write sin pi in terms of cos pi as, sin(pi) = √(1-cos²(pi)). Here, the value of cos pi is equal to lớn -1.

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What is the Value of Sin pi in Terms of Sec pi?

Since the sine function can be represented using the secant function, we can write sin pi as -√(sec²(pi) - 1)/sec pi. The value of sec pi is equal khổng lồ -1.