Cartesian Coordinate Systems - 3D Math Primer for Graphics and Game Development - page 22

The circumference of a unit circle is 2π, with π approximately equal to
3.14159265359. Therefore, 2π radians represents a complete revolution.
Since 360 o = 2π rad, 180 o = π rad. To convert an angle from radians
to degrees, we multiply by 180/π ≈ 57.29578, and to convert an angle from
degrees to radians, we multiply by π/180 ≈ 0.01745329. Thus,

(180/π) o ≈ 57.29578 o ,

1 rad =

Converting between
radians and degrees

1 o = (π/180) rad ≈ 0.01745329 rad.

In the next section, Table 1.2 will list several angles in both degree and
radian format.

1.4.4 Trig Functions
There are many ways to define the elementary trig functions. In this section,
we define them using the unit circle. In two dimensions, if we begin with
a unit ray pointing towards +x, and then rotate this ray counterclockwise
by an angle θ, we have drawn the angle in the standard position. (If the
angle is negative, rotate the ray in the other direction.) This is illustrated
in Figure 1.17.
The (x,y) coordinates of the endpoint of a ray thus rotated have spe-
cial properties and are so significant mathematically that they have been
assigned special functions, known as the cosine and sine of the angle:

Defining sine and cosine
using the unit circle cosθ = x, sinθ = y.

Figure 1.17
An angle in standard
position