Biomedical Engineering Reference
In-Depth Information
Trigonometric relationships
To solve Problem 1.2 and later ones, it is useful to remember some sim-
ple trigonometry. The principal functions for a triangle with a right angle
are shown in Figure 1.4.
A useful mnemonic device for understanding trigonometric functions
is the short phrase “soh-cah-toa.” Referring to the definitions given in
Figure 1.4, expanding this phrase reveals the following:
s
in =
o
pposite side length/
h
ypotenuse
c
os =
a
djacent side length/
h
ypotenuse
t
angent =
o
pposite side length/
a
djacent side length
A more formal expansion reveals the following trigonometric
identities:
sin α=
o
h
cos α=
a
h
tan α=
o
a
(sin × sin) + (cos × cos) = sin
2
+ cos
2
= 1
The values of these trigonometric functions for frequently occurring
angles are given in Table 1.4.
h
o
α
a
sin α =
o
/
h
cos α =
a
/
h
tan α =
o
/
a
1 cm = 10 cm
FIGUre 1.4
trigonometric relationships in a right-angle triangle.
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