Why is sin 360?

The question is likely asking: "Why is sin 360 degrees equal to zero?"

The value of sin 360° is zero because of its relationship to the unit circle.

Here's a breakdown:

• The Unit Circle: Imagine a circle with a radius of 1 centered at the origin (0,0) of a coordinate plane.

• Angles and Coordinates: An angle is formed by rotating a line from the positive x-axis counterclockwise. Where the line intersects the unit circle, we have coordinates (x, y).

• Sine and Cosine: The x-coordinate of that point is the cosine of the angle (cos θ), and the y-coordinate is the sine of the angle (sin θ).

• 360 Degrees: A 360-degree rotation brings us back to the starting point on the positive x-axis, which corresponds to the coordinates (1, 0).

• Therefore: Since the y-coordinate represents the sine of the angle, and at 360 degrees the y-coordinate is 0, then sin 360° = 0. As the reference states, "The value of sin 360° is equal to the y-coordinate (0)."

In summary, sin 360° = 0 because a 360-degree angle on the unit circle corresponds to the point (1, 0), and the y-coordinate of this point (which represents the sine value) is 0.