Why is the - sin of x the same as the sin of - x?

Sine is an odd function and presents positive values in the 1st and 2nd quadrants and negative values in the 3rd and 4th quadrants.

Step-by-step explanation:

-sin (x) = sin (-x)

This property is valid because the sine trigonometric function presents positive values in the first two quadrants and negative values in the third and fourth quadrants. The sine function is an odd function with symmetry with respect to the origin, which means that sin (x) and sin (-x) will always present opposite signs.