22
Chapter 1
•
Right Triangle Trigonometry
§1.3
24.
In Example 1.10 in Section 1.2, we found the exact values of all six trigonometric functions of
75
◦
. For example, we showed that cot 75
◦
=
radicallow
6
−
radicallow
2
radicallow
6
+
radicallow
2
. So since tan 15
◦
=
cot 75
◦
by the Cofunction
Theorem, this means that tan 15
◦
=
radicallow
6
−
radicallow
2
radicallow
6
+
radicallow
2
. We will now describe another method for finding the
exact values of the trigonometric functions of 15
◦
. In fact, it can be used to find the exact values
for the trigonometric functions of
θ
2
when those for
θ
are known, for any 0
◦
<
θ
<
90
◦
. The method
is illustrated in Figure 1.3.5 and is described below.
60
◦
30
◦
15
◦
7
.
5
◦
O
Q
1
A
B
C
P
Figure 1.3.5
Draw a semicircle of radius 1 centered at a point
O
on a horizontal line. Let
P
be the point on the
semicircle such that
OP
makes an angle of 60
◦
with the horizontal line, as in Figure 1.3.5. Draw
a line straight down from
P
to the horizontal line at the point
Q
. Now create a second semicircle
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 Fall '11
 Dr.Cheun
 Calculus, Trigonometry, Line segment, Elementary geometry

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