Final answer:
The terminal side of sin719° is in the IV quadrant, where the sine function has a negative sign because the y-coordinate of points in this quadrant is negative.
Step-by-step explanation:
To determine the quadrant of the terminal side and the sign of the sin function for sin719°, we first need to find the equivalent angle between 0° and 360° by subtracting multiples of 360° until we get an angle in that range. Since 719 - 360 = 359 and another 360° has not been completed, we are left with 359° as the equivalent angle. 359° is just shy of a full rotation, which places it in the IV quadrant.
The sign of trigonometric functions in each quadrant is determined by the x and y coordinates of points on the terminal side of the angle in the standard position. In the IV quadrant, the x-coordinate (representing the cosine function) is positive, and the y-coordinate (representing the sine function) is negative. Therefore, sin719° will have a negative sign. So the correct option is C) Quadrant: IV, Sign: Negative.