30
Chapter 1
•
Right Triangle Trigonometry
§1.4
negative
x
axis. So in Example 1.20, we see that 60
◦
is the reference angle for the nonacute
angle
θ
=
120
◦
; in Example 1.21, 45
◦
is the reference angle for
θ
=
225
◦
; and in Example
1.22, 30
◦
is the reference angle for
θ
=
330
◦
.
Example 1.24
28
◦
x
y
0
208
◦
928
◦
Figure 1.4.7
Let
θ
=
928
◦
.
(a)
Which angle between 0
◦
and 360
◦
has the same terminal side
(and hence the same trigonometric function values) as
θ
?
(b)
What is the reference angle for
θ
?
Solution: (a)
Since 928
◦
=
2
×
360
◦
+
208
◦
, then
θ
has the same ter
minal side as 208
◦
, as in Figure 1.4.7.
(b)
928
◦
and 208
◦
have the same terminal side in QIII, so the refer
ence angle for
θ
=
928
◦
is 208
◦
−
180
◦
=
28
◦
.
Example 1.25
Suppose that cos
θ
=−
4
5
. Find the exact values of sin
θ
and tan
θ
.
Solution:
We can use a method similar to the one used to solve Example 1.8 in Section 1.2. That is,
draw a right triangle and interpret cos
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This note was uploaded on 01/21/2012 for the course MAC 1130 taught by Professor Dr.cheun during the Fall '11 term at FSU.
 Fall '11
 Dr.Cheun
 Calculus, Trigonometry

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