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• Radians is the ratio of arc length $$(l)$$ to the radius $$(r)$$ of any circle is:

$\theta = \frac{{\color{Green}l}}{{\color{purple}r}}$

• For a circle of radius $$r$$, the angle $$\theta$$ will be one radian the corresponding arc length is of length $$r$$. This means that
$1 \mbox{ radian} \approx 57.2058 \mbox{ degrees}$

• Radians are a unit-less quantity.
• One complete revolution in radians.

\begin{eqnarray*} \theta &=& \frac{\text{Circumference of the circle}}{\text{radius}} \\ &=& \frac{2\pi {\cancel{r}}}{\cancel{r}} \\ &=& 2\pi \end{eqnarray*}

• Hence $$360^{\circ}=2\pi$$ or $$180^{\circ} =\pi$$.
• In calculus, (and other branches of mathematics) angles are measured entirely in radians.