Cartesian Coordinate Systems - 3D Math Primer for Graphics and Game Development - page 24

Figure 1.19
A more general
interpretation using (x, y)
coordinates rather than side
lengths

apply when θ is obtuse, since we cannot form a right triangle with an
obtuse interior angle. But by showing the angle in standard position and
allowing the rotated ray to be of any length r (Figure 1.19), we can express
the ratios using x, y, and r:

cosθ = x/r, sinθ = y/r, tanθ = y/x,

secθ = r/x, cscθ = r/y, cotθ = x/y.

Table 1.2 shows several different angles, expressed in degrees and radi-
ans, and the values of their principal trig functions.

1.4.5 Trig Identities
In this section we present a number of basic relationships between the trig
functions. Because we assume in this topic that the reader has some prior
exposure to trigonometry, we do not develop or prove these theorems. The
proofs can be found online or in any trigonometry textbook.
A number of identities can be derived based on the symmetry of the
unit circle:

sin(−θ) = − sinθ, cos(−θ) = cosθ, tan(−θ) = − tanθ,

Basic identities related
to symmetry

π
2

π
2

π
2

sin − θ = cosθ, cos − θ = sinθ, tan − θ = cotθ.