which of the following is true of the location of the terminal side of an angle, $\theta$, whose sine value…

Explanation:

Step1: Recall sine - value and reference angle relationship

We know that $\sin\theta=\frac{1}{2}$, and the reference - angle formula for $\sin\theta$ is $\sin\alpha =|\sin\theta|$, where $\alpha$ is the reference angle. Since $\sin\theta=\frac{1}{2}$, we find the reference angle $\alpha$ such that $\sin\alpha=\frac{1}{2}$. The angle whose sine is $\frac{1}{2}$ in the first - quadrant is $\alpha = 30^{\circ}$ (or $\frac{\pi}{6}$ radians).

Step2: Determine the quadrants where sine is positive

The sine function is positive in Quadrant I and Quadrant II. That is, if $\sin\theta>0$, then the terminal side of the angle $\theta$ lies in either Quadrant I or Quadrant II.

Answer:

$\theta$ has a reference angle of $30^{\circ}$ and is in Quadrant I or II.