Game Development Reference
In-Depth Information
Trigonometric Ratios
You measure angles using degrees and radians. You usually measure the lengths
of sides using real numbers. You relate the measurements of angles to the
measurements of sides using ratios. A set of six such ratios constitute the primary
trigonometric ratios. You have already examined the ratio that generates the sine
of the angle (theta)
.
If you extend the discussion that began with the sine of the angle
, you can then
work forward to explore the ratios defined for the cosine and tangent of
. You
then move on from there to explore the ratios defined for cotangent, secant, and
cosecant. Figure 12.8 illustrates the standard form of the right triangle with the
sides explicitly identified.
Each of the trigonometric ratios provides information on the angle
. In this
respect, then, you refer to ''the sine of theta,'' ''the cosine of theta,'' and so on,
and in each instance, the ratio that you explore involves a relation between two of
the three sides of a right triangle. Table 12.2 details the ratios.
Figure 12.8
The opposite and adjacent sides and the hypotenuse of the right triangle generate the trigonometric
ratios.
Table 12.2
Trigonometric Ratios
Item
Ratio
Mnemonic
opposite
hypotenuse
O
H
Sine
sin y ¼
adjacent
hypotenuse
A
H
Cosine
cos y ¼
Tangent
opposite
adjacent
O
A
tan
y ¼
Cotangent
adjacent
opposite
A
O
cot
y ¼
Secant
hypotenuse
adjacent
H
A
sec
y ¼
Cosecant
hypotenuse
opposite
H
O
csc
y ¼
