# Trigonometry

## Worked Examples

## Radians

So far, we have been using degrees to measure angles. Another unit of measurement is*radians*.

**One radian**is the angle which creates an arc the same lenth as $r$, the radius of the circle.

How do we go between degrees and radians?

Recall that the angle created when we go around the circle is $360^{\circ}$. The arc created is the circumference, i.e. $2\pi r$, so the measurement of that angle is also $2\pi$ radians. So, we get: $$360^{\circ}=2\pi \hspace{3 mm} \text{radians}$$ This tells us that $1^{\circ}=2\pi/360 \hspace{3 mm} \text{rad}$, or: $$\theta^{\circ}=\frac{2\pi}{360}\times \theta \hspace{3 mm} \text{rad}$$ And similarly: $$\theta\hspace{3 mm} \text{rad}=\frac{360}{2 \pi}\times \theta^{\circ}$$