EXAMPLE:
◦
(a) Find angles that are coterminal with the angle θ = 30
in standard position.
π
(b) Find angles that are coterminal with the angle θ =
in standard position.
3
Solution:
◦
◦
(a) To find positive angles that are coterminal with θ, we add any multiple of 360
to 30
. Thus
◦
◦
◦
◦
◦
◦
30
+ 360
= 390
,
30
+ 720
= 750
,
etc.
◦
are coterminal with θ = 30
. To find negative angles that are coterminal with θ, we subtract
◦
◦
any multiple of 360
from 30
. Thus
◦
◦
◦
◦
◦
◦
30
360
=
330
,
30
720
=
690
,
etc.
are coterminal with θ.
(b) To find positive angles that are coterminal with θ, we add any multiple of 2π to π/3. Thus
π
7π
π
13π
+ 2π =
,
+ 4π =
,
etc.
3
3
3
3
are coterminal with θ = π/3. To find negative angles that are coterminal with θ, we subtract
any multiple of 2π from π/3. Thus
π
5π
π
11π
2π =
,
4π =
,
etc.
3
3
3
3
are coterminal with θ.
EXAMPLE:
◦
(a) Find angles that are coterminal with the angle θ = 62
in standard position.
5π
(b) Find angles that are coterminal with the angle θ =
in standard position.
6
3