Radian Measure
Radians?
- 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.
To do
-
Radian Measure worksheet (sigma Mathematics and Statistics Support Coventry University)
More info
- Measuring angles video (MathsCasts)
- Degrees and radians quick reference (mathcentre)
- Radians and degrees video (Khan Academy)