What are the operating signs of sine in Quadrant 3 of the unit circle?

In the context of the unit circle and trigonometric functions, each quadrant has specific signs associated with the values of sine, cosine, and tangent. In Quadrant 3, which is located where both x (the cosine) and y (the sine) coordinates of points on the unit circle are negative, we find that the sine function, representing the y-coordinate, is also negative.

To understand this further, recall that the unit circle is centered at the origin (0,0) with a radius of 1. As you move to the left of the y-axis and downward from the x-axis, you are in Quadrant 3. Here, all points have negative y-values, which means that the sine of any angle corresponding to this quadrant will likewise yield a negative value. Thus, the operating sign of the sine function in Quadrant 3 is indeed negative.

This reinforces the idea that when determining the values of trigonometric functions in different quadrants, one must consider both the position of the angle and the signs of the coordinates that correspond to those angles.