Question

An angle in standard position measures 5π/6
radians and intercepts a circle with center at (0,0) and radius 4. Find the length of the arc determined by the points of intersection.
HELP PLEASE :(

Answer 1

So how much around a circle is 5pi/6?

Answer 2

well let's see

Answer 3

5/6 of a \(\pi\)
that is

so, we know the angle, "in radians"
we also know the radius of the circle it intercepts
so, how long is the "arc"?

well \(\large \textit{arc's length}=s=r\theta\qquad
\begin{cases}
r=radius\\
\theta=\textit{angle in radians}
\end{cases}
\)