28
Chapter 1
•
Right Triangle Trigonometry
§1.4
Example1.23
x
y
0
0
◦
(1
,
0)
90
◦
(0
,
1)
180
◦
(
−
1
,
0)
270
◦
(0
,
−
1)
Figure 1.4.6
Find the exact values of all six trigonometric functions of 0
◦
, 90
◦
,
180
◦
, and 270
◦
.
Solution:
These angles are different from the angles we have con
sidered so far, in that the terminal sides lie along either the
x
axis
or the
y
axis. So unlike the previous examples, we do not have any
right triangles to draw.
However, the values of the trigonometric
functions are easy to calculate by picking the simplest points on their
terminal sides and then using the definitions in formulas (1.2) and
(1.3).
For instance, for the angle 0
◦
use the point (1
,
0) on its terminal
side (the positive
x
axis), as in Figure 1.4.6. You could think of the
line segment from the origin to the point (1
,
0) as sort of a degenerate
right triangle whose height is 0 and whose hypotenuse and base have
the same length 1. Regardless, in the formulas we would use
r
=
1,
x
=
1, and
y
=
0. Hence:
sin 0
◦
=
y
r
=
0
1
=
0
cos 0
◦
=
x
r
=
1
1
=
1
tan 0
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 Fall '11
 Dr.Cheun
 Calculus, Trigonometry, Angles, Right triangle, Hypotenuse, triangle, 1 sec, −1, 0 Sec

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