Question

What is the arc length of an angle of 2π 3 radians formed on the unit circle?

Answer 1

recall, the Unit Circle is called like so because it has a radius of 1.

so, what's the arc for an angle of 2π/3 and a radius of 1?


`\bf \textit{arc's length}\\\\ s=r\theta \quad \begin{cases} r=radius\\ \theta =angle~in\\ \qquad radians\\ ------\\ r=1\\ \theta = (2\pi )/(3) \end{cases}\implies s=1\cdot (2\pi )/(3)\implies s=(2\pi )/(3)`