Radians

These are little blighters used to describe the angles of circles. Like degrees, they can be used to express arc widths, or can be used in equations (especially trig equations). Basically they're just like degrees, but are based on π and the radius of the circle (hence radian). Imagine a line from the centre to any point on the circle. That's a radius. Then, in any direction, draw an arc around the surface of the circle with the same length as the radius. Stop. Draw a radius from this point back to the centre.

The angle subtended is one radian.

There are 360 degrees in a circle and one degree really isn't very large.

A radian is much bigger (around 57 degrees). Every circle has 2π radians, like every circle has 360°. 180° is therefore π radians.

Most calculations involving radians will also involve fractions. Using π enables you to be exact without lots of fiddly decimals. The same is true of fractions. In some ways then, using radians is satisfyingly precise.

It is also easy to convert one to the other.

360° = 2π radians

Therefore

1° = 2π radians/360.

and

say

12° = (2π/360) x 12

= 24π/360

= π/15

and it's usually sufficient to leave it like this for C2. At other levels you might want to do the calculation to n dps or whatever.

Similarly

2π radians = 360°

1 radian = 360/2π

and

so

3 radians = (360/2π) x 3.

Easy.