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, us will talk about the approaches to uncover the worth of sin pi v examples.
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What is the value of Sin pi?
The value of sin pi is 0. Sin pi can likewise be expressed utilizing the indistinguishable of the provided angle (pi) in degrees (180°).
We know, using radian to degree conversion, θ in levels = θ in radians × (180°/pi)⇒ pi radians = pi × (180°/pi) = 180° or 180 degrees∴ sin pi = sin π = sin(180°) = 0
For sin pi, the angle pi lies ~ above the an unfavorable x-axis. Thus, sin pi value = 0Since the sine duty is a routine function, we have the right to represent sin pi as, sin pi = sin(pi + n × 2pi), n ∈ Z.⇒ sin pi = sin 3pi = sin 5pi , and so on.Note: Since, sine is an odd function, the value of sin(-pi) = -sin(pi) = 0.
Methods to uncover Value the Sin pi
The worth of sin pi is provided as 0. We can find the worth of sin pi by:Using Unit CircleUsing Trigonometric Functions
Sin pi using Unit Circle
To uncover the value of sin π utilizing the unit circle:Rotate ‘r’ anticlockwise to form pi angle v the hopeful x-axis.The sin that pi amounts to the y-coordinate(0) the the point of intersection (-1, 0) of unit circle and r.
Hence the worth of sin pi = y = 0
Sin pi in regards to 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: due to the fact that pi lies top top the negative x-axis, the final value that sin pi is 0.
We have the right to use trigonometric identities to stand for 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
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FAQs top top Sin pi
What is Sin pi?
Sin pi is the value of sine trigonometric function for an angle same to pi radians. The value of sin pi is 0.
How to discover Sin pi in state of other Trigonometric Functions?
Using trigonometry formula, the value of sin π have the right to be provided in state of other trigonometric features as:± √(1-cos²(pi))± tan(pi)/√(1 + tan²(pi))± 1/√(1 + cot²(pi))± √(sec²(pi) - 1)/sec(pi)1/cosec(pi)
☛ likewise check: trigonometric table
How to discover the worth of Sin pi?
The worth of sin pi can be calculate by constructing an edge of π radians v the x-axis, and also then finding the coordinates of the corresponding allude (-1, 0) top top the unit circle. The value of sin pi is equal to the y-coordinate (0). ∴ sin pi = 0.
What is the worth of Sin pi in terms of Cos pi?
Using trigonometric identities, we have the right to write sin pi in regards to cos pi as, sin(pi) = √(1-cos²(pi)). Here, the value of cos pi is equal to -1.
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What is the value of Sin pi in terms of Sec pi?
Since the sine duty 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 to -1.