SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
The details of the solution are as follows:
[tex]\begin{gathered} Arc\text{ length =}\frac{\theta}{360^0}\text{ x 2}\pi\text{ r} \\ where\text{ arc length = 4 units} \\ and\text{ the radius, r = 3 units} \end{gathered}[/tex][tex]\begin{gathered} puttin\text{g the values, we have that:} \\ \text{4 =}\frac{\theta}{360^0}\text{ x 2 x }\pi\text{ x 3} \\ Then,\text{ we have that:} \end{gathered}[/tex][tex]\begin{gathered} cross\text{ - multiply, we have that:} \\ 4\text{ x 360}^0\text{ = }\theta\text{ x 6}\pi \\ 1440^0\text{ = }\theta\text{ x 6}\pi \end{gathered}[/tex][tex]\begin{gathered} Divide\text{ both sides by 6}\pi\text{, we have that:} \\ \theta\text{ =}\frac{1440^0}{6\pi}=\frac{240}{\pi} \end{gathered}[/tex][tex]\begin{gathered} Note\text{ that:} \\ 2\pi\text{ }rad\text{ = 360}^0 \end{gathered}[/tex][tex]\begin{gathered} 2\pi rad\text{ = 360}^0 \\ ?\text{ = }\frac{240}{\pi}=\text{ 76}\frac{4}{11}\text{ }^0\text{ = }\frac{840^0}{11^} \end{gathered}[/tex][tex]?\text{ =}\frac{2\pi\text{ rad x }\frac{840}{11}}{360}[/tex][tex]?\text{ = }\frac{\pi\text{ rad}}{180}\text{ x }\frac{840}{11}[/tex][tex]?\text{ =}\frac{14}{33}\text{ }\pi\text{ rad }\approx\text{ 0.42 }\pi\text{ rad \lparen correct to 2 decimal places\rparen}[/tex]
CONCLUSION:
The measure of the central angle ( in radians) =
[tex]0.42\pi\text{ \lparen correct to 2 decimal places\rparen}[/tex]
