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

• A. $>0$
• B. $1$
• C. $<0$
• D. $0$

Answer: (A)

Verified step by step guidance

1. Recall the definition of the sine function in terms of the unit circle: for an angle \( \theta \), \( \sin(\theta) \) represents the y-coordinate of the point on the unit circle corresponding to \( \theta \).
2. Identify the location of Quadrant II on the coordinate plane: Quadrant II is where the x-values are negative and the y-values are positive.
3. Since \( \theta \) is in Quadrant II, the y-coordinate of the point on the unit circle (which equals \( \sin(\theta) \)) must be positive.
4. Therefore, \( \sin(\theta) > 0 \) when \( \theta \) is in Quadrant II.
5. Summarize that the value of \( \sin(\theta) \) for an angle in Quadrant II is positive, so the correct choice is \( \sin(\theta) > 0 \).