Question

If the arc length of a sector in the unit circle is 3 radians, what is the measure of the angle of the sector?

Answer 1

the above said.... we know the arc is 3 units, meters or feet or who knows, and is in the Unit Circle, the Unit Circle is called like so because its radius is exactly 1 unit long.


`\bf \textit{arc's length}\\\\ s=r\theta \quad \begin{cases} r=radius\\ \theta =angle~in\\ \qquad radians\\ ------\\ r=1\\ s=3 \end{cases}\implies 3=1\theta \implies \cfrac{3}{1}=\theta \implies \stackrel{radians}{3}=\theta`