Angle Measure Worksheet With Answers - Section 6.1 Page 4
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10EXAMPLE:
◦
(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
Solution:
◦
◦
(a) To find positive angles that are coterminal with θ, we add any multiple of 360
to 62
. Thus
◦
◦
◦
◦
◦
◦
62
+ 360
= 422
,
62
+ 720
= 782
,
etc.
◦
are coterminal with θ = 62
. To find negative angles that are coterminal with θ, we subtract
◦
◦
any multiple of 360
from 62
. Thus
◦
◦
◦
◦
◦
◦
62
360
=
298
,
62
720
=
658
,
etc.
are coterminal with θ.
(b) To find positive angles that are coterminal with θ, we add any multiple of 2π to 5π/6. Thus
5π
17π
5π
29π
+ 2π =
,
+ 4π =
,
etc.
6
6
6
6
are coterminal with θ = 5π/6. To find negative angles that are coterminal with θ, we subtract
any multiple of 2π from 5π/6. Thus
5π
7π
5π
19π
2π =
,
4π =
,
etc.
6
6
6
6
are coterminal with θ.
◦
◦
EXAMPLE: Find an angle with measure between 0
and 360
that is coterminal with the angle
◦
of measure 1290
in standard position.
◦
◦
Solution: We can subtract 360
as many times as we wish from 1290
, and the resulting angle
◦
◦
◦
◦
◦
will be coterminal with 1290
. Thus, 1290
360
= 930
is coterminal with 1290
, and so is
◦
◦
◦
the angle 1290
2(360)
= 570
.
◦
◦
◦
◦
To find the angle we want between 0
and 360
, we subtract 360
from 1290
as many times
◦
◦
as necessary. An efficient way to do this is to determine how many times 360
goes into 1290
,
that is, divide 1290 by 360, and the remainder will be the angle we are looking for. We see
◦
that 360 goes into 1290 three times with a remainder of 210. Thus, 210
is the desired angle
(see the Figures below).
EXAMPLE:
(a) Find an angle between 0 and 2π that is coterminal with 100.
◦
◦
◦
(b) Find an angle between 0
and 360
that is coterminal with
3624
.
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