why does sin(-x) equal to -sin(x)?

Answer 1

The sine function is an odd function, which means that it has symmetry around the origin. This means that for any angle x, sin(-x) is equal to -sin(x) because the negative angle (-x) corresponds to the reflection of the angle x across the origin.

Another way to understand this relationship is to consider the unit circle. The sine of an angle x is equal to the y-coordinate of the point on the unit circle corresponding to that angle. Reflecting the angle across the origin changes the sign of the y-coordinate, resulting in sin(-x) being equal to -sin(x).