Consider the equation $\sin \theta$. If $\theta$ is an angle in Quadrant IV, what is the value of $\sin \theta$?

• A. It is negative.
• B. It is zero.
• C. It is positive.
• D.

Answer: (A)

Verified step by step guidance

1. Recall the definition of the sine function: for an angle \( \theta \), \( \sin(\theta) \) represents the y-coordinate of the point on the unit circle corresponding to \( \theta \).
2. Identify the quadrant where \( \theta \) lies. Since \( \theta \) is in Quadrant IV, this means the angle is between 270° and 360° (or between \( \frac{3\pi}{2} \) and \( 2\pi \) radians).
3. Understand the sign of sine in each quadrant: sine is positive in Quadrants I and II, and negative in Quadrants III and IV because the y-values are below the x-axis in these quadrants.
4. Since \( \theta \) is in Quadrant IV, the y-coordinate (and thus \( \sin(\theta) \)) is negative.
5. Therefore, the value of \( \sin(\theta) \) when \( \theta \) is in Quadrant IV is negative.