3. The angle whose terminal side passes through \( \left(\frac{\sqrt{3}}{2},-\frac{1}{2}\right) \) is in the ___ quadrant.

The angle whose terminal side passes through \( \left(\frac{\sqrt{3}}{2},-\frac{1}{2}\right) \) lies in the fourth quadrant. In this quadrant, the x-coordinate is positive, while the y-coordinate is negative. So, if you're plotting points, just remember: quadrant IV is where you can find positive x values hanging out with negative y values, perfect for those angles between 270° and 360°! A fun twist to this angle intrigue is how it relates to famous angles in trigonometry. The coordinates \( \left(\frac{\sqrt{3}}{2},-\frac{1}{2}\right) \) align with the reference angle of 30° (or \(\frac{\pi}{6}\) radians), making it super useful for calculating sine and cosine values. For \( \theta \) in the fourth quadrant, you really want to remember that sine values are negative, while cosine values are positive—just like this point!