Game Development Reference
In-Depth Information
Figure 12.11
Calculate the value of the adjacent side.
Table 12.3
Ratios Applied to Other Angles
Values for 30
8
Values for 60
8
hypotenuse
¼
p
2
sin 30
¼
opposite
hypotenuse
¼
sin 60
¼
opposite
1
2
hypotenuse
¼
p
2
cos 30
¼
adjacent
cos 60
¼
adjacent
hypotenuse
¼
1
2
adjacent
¼
p
1
tan 30
¼
opposite
adjacent
¼
1
tan 60
¼
opposite
p
opposite
¼
p
1
cot 30
¼
adjacent
cot 60
¼
adjacent
opposite
¼
1
p
hypotenuse
adjacent
hypotenuse
adjacent
sec 30
¼
2
sec 60
¼
2
1
¼
¼
p
hypotenuse
opposite
hypotenuse
opposite
csc 30
¼
2
1
csc 60
¼
2
3
¼
¼
p
you can employ the Pythagorean theorem to calculate values to use in the tri-
gonometric ratios.
If you apply the Pythagorean theorem to slightly modified versions of the triangle
Figure 12.10 illustrates, you can readily arrive at the trigonometric ratios for two
other angles that prove important. These are the values that correspond to 30
8
and 60
. Table 12.3 lists the calculations that result when you the apply the
trigonometric ratios to the information Figure 12.11 provides using an equi-
lateral triangle.
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