In a circle with radius 4 , an angle intercepts an arc of length $2 \pi$. Find the angle in radians in simplest form.

Step 1 ：Given a circle with radius 4, an angle intercepts an arc of length \(2 \pi\). We are asked to find the angle in radians in simplest form.

Step 2 ：The formula to calculate the length of an arc is given by \(l = r \theta\), where \(l\) is the length of the arc, \(r\) is the radius of the circle, and \(\theta\) is the angle in radians.

Step 3 ：We can rearrange this formula to solve for \(\theta\): \(\theta = \frac{l}{r}\).

Step 4 ：In this case, \(l = 2\pi\) and \(r = 4\), so we can substitute these values into the formula to find the angle.

Step 5 ：\(\theta = \frac{2\pi}{4} = \frac{\pi}{2}\).

Step 6 ：So, the angle in radians in simplest form is \(\boxed{\frac{\pi}{2}}\).