8.3 - Radian Measure Quiz

Use the equation $$\pi=180\degree$$ to help you do the conversion.

$$\pi=180\degree$$

So

$$1=\frac{180\degree}{\pi}$$

$$1=57.29577...\degree$$

$$1=57.3\degree\ \left(1d.p.\right)$$

This gives us a sense of how big 1 radian is in terms of degrees.

Note in the diagram that for a fixed radius of 5 units,

as the angle increases, the arc length increases as well.

This shows that the arc length is directly proportional to the angle (for a fixed radius).

Recall:

$$\theta=\frac{s}{r}$$  

i.e. $$\theta=\frac{arc\ length}{radius}$$

There is no degree symbol on the angle. Hence, it is measured in radian in this case.