Which of the following is a negative angle formula for sine?

The formula that describes the sine of a negative angle is grounded in the properties of the sine function as an odd function. An odd function is one that satisfies the property ( f(-x) = -f(x) ).

In this case, sine is classified as an odd function, which leads us to the correct relationship: the sine of a negative angle is equal to the negative sine of the corresponding positive angle. This relationship can be expressed mathematically as sin(-x) = -sin(x).

This means that if you take any angle ( x ) and find its sine, the sine of its negative will yield the opposite value. For instance, if ( sin(30^\circ) = 0.5 ), then ( sin(-30^\circ) ) will equal (-0.5), illustrating how the function behaves symmetrically about the origin on a graph.

The definitions of sine provided in the other options do not hold true for the sine function and fail to reflect its odd function nature. The correct answer reinforces the understanding of how sine behaves with respect to angle transformations, which is crucial for solving various trigonometric problems.