suppose y = sin x. what is the x - value between 0 and $\frac{pi}{2}$ that corresponds to a y - value of…

Explanation:

Step1: Set up the equation

Given $y = \sin x$ and $y=\frac{1}{2}$, we set up $\sin x=\frac{1}{2}$.

Step2: Recall sine - function values

We know that for $x\in[0,\frac{\pi}{2}]$, $\sin x$ has a well - known value. The angle $x$ for which $\sin x=\frac{1}{2}$ in the interval $[0,\frac{\pi}{2}]$ is based on the unit - circle definition of the sine function. The sine of an angle in the first quadrant that gives $\frac{1}{2}$ is $x = \frac{\pi}{6}$.

Answer:

$\frac{\pi}{6}$