Yes, the sine of pi (sin π) is exactly 0.
Here's why:
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Unit Circle Definition: In the unit circle, the sine of an angle is represented by the y-coordinate of the point where the terminal side of the angle intersects the circle. An angle of π radians (180 degrees) places the point on the unit circle at (-1, 0). Therefore, sin(π) = 0.
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Graphical Representation: The graph of the sine function, y = sin(x), crosses the x-axis at x = 0, x = π, x = 2π, and so on. This visually demonstrates that sin(π) = 0.
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Mathematical Identity: sin(π) = 0 is a fundamental trigonometric identity. It's a universally accepted mathematical fact.
| Angle (radians) | Angle (degrees) | Sine Value |
|---|---|---|
| 0 | 0° | 0 |
| π/2 | 90° | 1 |
| π | 180° | 0 |
| 3π/2 | 270° | -1 |
| 2π | 360° | 0 |
