Definition y
Radian: The
length of the
arc above the
angle divided
by the radius of
the circle.
1
r

-1
-1
s
  ,  in radians
r
s
1
x
Definition y
Unit Circle:
the circle with
radius of 1
unit
If r=1,  =s
1
1

-1
-1
s
  ,  in radians
1
s
1
x
Definition
The radian measure of an
angle is the distance traveled
around the unit circle. Since
circumference of a circle is
2  r and r=1, the distance
around the unit circle is 2 
Important Idea
If a circle contains 360° or
2 radians, how many
radians are in 180°
Use to change
rads to degrees
Use
to
change
rads

•
180° degrees to rads
180°
•
 rads
Try This
Change 240° to radian
measure in terms of .
4
rads
3
Try This
7

Change
radians to
8
degree measure.
157.5°
Try This
Change 3 radians to
degree measure.
171.89°
Definition
Terminal Side
y
Vertex
A
Initial Side
x
Angle A
is in
standard
position
Definition
y
A
x
If the
terminal
side
moves
counterclockwise,
angle A is
positive
Definition
y
A
x
If the
terminal
side
moves
counterclockwise,
angle A is
positive
Definition
y
A
x
If the
terminal
side
moves
counterclockwise,
angle A is
positive
Definition
y
A
x
If the
terminal
side
moves
clockwise,
angle A is
negative
Definition
y
A
x
If the
terminal
side
moves
clockwise,
angle A is
negative
Definition
y
A
x
If the
terminal
side
moves
clockwise,
angle A is
negative
Definition
y
A
x
If the
terminal
side
moves
clockwise,
angle A is
negative
Definition
y
A
If the
terminal
side is on
x an axis,
angle A is a
quadrantel
angle
Definition
y
A
If the
terminal
side is on
x an axis,
angle A is a
quadrantel
angle
Definition
y
A
If the
terminal
side is on
x an axis,
angle A is a
quadrantel
angle
Definition
y
A
If the
terminal
side is on
x an axis,
angle A is a
quadrantel
angle
Definition 
The
quadrantal
angles in
radians
2

0
2
3
2
Definition 
The
quadrantal
angles in
radians
2

0
2
3
2
Definition 
The
quadrantal
angles in
radians
2

0
2
3
2
Definition 
2
The
quadrantal
0
angles in

2
radians
The terminal side is on an
axis.
Definition
Coterminal Angles: Angles
that have the same terminal
side.
Important Idea
To find coterminal angles,
simply add or subtract
either 360° or 2  radians
to the given angle or any
angle that is already
coterminal to the given
angle.
Analysis
30° and
390° have
the same
terminal
side,
therefore,
the angles
are
coterminal
y
30°
x
y
390°
x
Analysis
30° and
750° have
the same
terminal
side,
therefore,
the angles
are
coterminal
y
30°
x
y
750°
x
Analysis
30° and
1110° have
the same
terminal
side,
therefore,
the angles
are
coterminal
y
30°
x
y
1110°
x
Analysis
30° and
-330° have
the same
terminal
side,
therefore,
the angles
are
coterminal
y
30°
x
y
-330°
x
Try This
Find 3 angles coterminal
with 60°
420°,780° and -300°
Try This
Find two positive angle and
one negative angle
coterminal with  5
6
radians.
19
7
17

and

,
6
6
6