Final answer:
The given statement is false because there is no general equality where sin(-x) = -cos(x). Sine and cosine correspond to different coordinates on the unit circle and have different symmetrical properties regarding negative angles.
Step-by-step explanation:
The statement sin(-x) = -cos(x) is false. To understand why, we should look at the basic properties of sine and cosine functions and their relationship to angles. Recall that sin(x) represents the y-coordinate of the point on the unit circle corresponding to an angle x, and cos(x) represents the x-coordinate of the same point.
Since sine and cosine are related to orthogonal axes, there is no general equality where the sine of one angle equals the negative cosine of that angle.
Instead, what holds true is the property of odd and even functions for sine and cosine. Sin(-x) is equal to -sin(x) because sine is an odd function. Conversely, cos(-x) is equal to cos(x) because cosine is an even function. Therefore, if we take the negative angle of x, the sine function will output the negative value, and the cosine function will output the same value as if it were the positive angle.