Download this document - Toolbox PRO V2

282 Chapter 4 Trigonometry
θ =
π
2
Quadrant II
π
< θ < π
2
Quadrant I
0 < θ <
π
2
θ = π
θ = 0
Quadrant III Quadrant IV
π < θ <
3π
3π
< θ < 2π
2 2
The phrase “the terminal side
of lies in a quadrant” is often
abbreviated by simply saying
that “ lies in a quadrant.” The
terminal sides of the “quadrant
angles” 0, 2, , and 32 do
not lie within quadrants.
FIGURE 4.8
Two angles are coterminal if they have the same initial and terminal sides. For
instance, the angles 0 and are coterminal, as are the angles 6 and 136. You can
find an angle that is coterminal to a given angle by adding or subtracting (one
revolution), as demonstrated in Example 1. A given angle has infinitely many
coterminal angles. For instance, is coterminal with
6 2n
where n is an integer.
2
6
θ =
3 π 2
2
You can review operations
involving fractions in Appendix
A.1.
Example 1
Sketching and Finding Coterminal Angles
a. For the positive angle 136, subtract 2 to obtain a coterminal angle
See Figure 4.9.
6 2
6 .
13
b. For the positive angle 34, subtract 2 to obtain a coterminal angle
See Figure 4.10.
4 2 5
4 .
3
c. For the negative angle 23, add 2 to obtain a coterminal angle
2
See Figure 4.11.
3 2 4
3 .
π
π
2
θ = 13 π
6 6
π
3π
2
0
π
FIGURE 4.9 FIGURE 4.10 FIGURE 4.11
Now try Exercise 27.
π
2
3π
2
θ =
3π
4
−
5π
4
0
π
4π
3
π
2
θ = −
2π
3
3π
2
0