Now that you know what a radian is, let’s calculate how many radians there
are in a circle. You may remember the Greek symbol p (pi) from your
school days. It’s a wellknown and frequently used mathematical constant,
and has a value of 3.14159 (to five decimal places). You can use pi to cal

culate the circumference of a circle — the distance around the entire
perimeter — using the equation:
(1.39)
Using this equation to determine the perimeter of a unit circle gives the
number of radians in a circle. That’s because the number of radians in a cir

cle is the length of the perimeter of a circle with a radius of 1. So we just
substitute 1 for r in equation (1.39) to get:
(1.40)
Therefore, there are 2 p radians in every circle.
z
TIP Now that you know how many radians make up a circle, you can convert
between radians and degrees if you ever have to. There are 360 degrees in a
circle, so that means:
360º = 2 p rads
Dividing both sides by 360 we get:
1º=2p /360 rads
Angles are usually denoted using the Greek letter theta, which looks like
this: q.
Triangles
A triangle consists of three line segments connected at their ends. A trian

gle’s inner angles always add up to p radians (180 degrees). Figure 1.9
shows the different types of triangles you can encounter.
12  Chapter 1
Mathematics
2perimeter rp=
22(1)2perimeter r num radianspp p== ==
Figure 1.9. Different types of triangles