The sine of 0 degrees (sin 0°) is zero.
Understanding the Sine Function
The sine function, often written as sin(x), is a fundamental trigonometric function that relates an angle of a right triangle to the ratio of the length of the opposite side to the length of the hypotenuse. In the context of the unit circle, sin(θ) represents the y-coordinate of the point on the circle corresponding to an angle θ.
Sin 0° Explained
According to the provided reference, sin 0° = 0.
- Unit Circle Perspective: Imagine an angle of 0 degrees on the unit circle. The point on the circle that corresponds to 0 degrees is (1, 0). Since sine represents the y-coordinate, sin 0° = 0.
- Right Triangle Perspective: Consider a right triangle where one of the angles is approaching 0 degrees. As the angle gets closer to 0, the length of the side opposite to that angle also approaches 0. Since sine is the opposite side divided by the hypotenuse, as the opposite side approaches 0, the sine of the angle also approaches 0.
Table of Common Sine Values
| Angle (Degrees) | Sine Value |
|---|---|
| 0° | 0 |
| 30° | 1/2 |
| 45° | √2/2 |
| 60° | √3/2 |
| 90° | 1 |
Conclusion
Therefore, based on trigonometric principles and the reference provided, the sine of zero degrees equals zero.
