1.
2.
3.
4.
5.
Objectives:
Be able to draw an angle in standard position and find the
positive and negative rotations.
Be able to convert degrees into radians and radians into
degrees.
Be able to find complementary and supplementary angles in
radians and degrees.
Be able to find co-terminal angles in radians and degrees
Be able to find the arc length and Area of a sector.
Critical Vocabulary:
Positive Rotation, Negative Rotation, Standard Position,
Quadrantal Angle, Co-terminal, Degrees, Radians
Ray: Starts at a point and extends indefinitely in one direction.
A
Angle: Two rays that are drawn with a
common vertex
B
C
B
A
Positive Rotation: The angle formed from the initial side to the
terminal side rotating counter- clockwise.  
Negative Rotation: The angle formed from the initial side to the
terminal side rotating clockwise.   
Standard Position: The vertex of an angle is located at the origin
Initial Side
Lies in Quadrant: The location of the terminal side.
 (theta) = the angle measurement.
1.  = 360 degrees = 1 revolution
2.  = 90 degrees = ¼ revolution
Reference Angle:
The angle between the
terminal ray and the xaxis.
3.  = 180 degrees = ½ revolution
4.  = 260 degrees = 13/18 revolution
Example 1: Draw an angle of 315° in standard position
Initial Side
 = 315 degrees
 = 315 degrees
 = -45 degrees
Lies in Quadrant 4
Reference: 45 degrees
 (theta) = the angle measurement.
1.  = 360 degrees = 1 revolution
2.  = 90 degrees = ¼ revolution
3.  = 180 degrees = ½ revolution
4.  = 260 degrees = 13/18 revolution
Example 2: Draw an angle of -125° in standard position
Initial Side
 = -125 degrees
 = 235 degrees
 = -125 degrees
Lies in Quadrant 3
Reference: 55 degrees
 (theta) = the angle measurement.
1.  = 360 degrees = 1 revolution
2.  = 90 degrees = ¼ revolution
3.  = 180 degrees = ½ revolution
4.  = 260 degrees = 13/18 revolution
Example 3: Draw an angle of 460° in standard position
 = 460 degrees
Initial Side
 = 100 degrees
 = -260 degrees
Lies in Quadrant 2
Reference: 80 degrees
 (theta) = the angle measurement.
1.  = 360 degrees = 1 revolution
2.  = 90 degrees = ¼ revolution
3.  = 180 degrees = ½ revolution
4.  = 260 degrees = 13/18 revolution
Example 4: Draw an angle of -1020° in standard position
 = -1020 degrees
Initial Side
 = 60 degrees
 = -300 degrees
Lies in Quadrant 1
Reference: 60 degrees
 (theta) = the angle measurement.
1.  = 360 degrees = 1 revolution
2.  = 90 degrees = ¼ revolution
3.  = 180 degrees = ½ revolution
4.  = 260 degrees = 13/18 revolution
Terminal
Side
Example 5: Draw an angle of -270° in standard position
 = -270 degrees
Initial Side
 = 90 degrees
 = -270 degrees
Quadrantal Angle
Quadrantal Angle: Terminal side is located on an axis
Page 862-863 #3-9 all, 14
Directions (#3-9):
1.
2.
3.
4.
5.
Draw the Angle in Standard Position
How many complete rotations
What are Alpha and Beta
What Quadrant does the Angle Lie in
What is the Reference Angle
Page 862 -863 #3, 4, 6-9 all, 14
3.
4.
6.
7.
8.
Rotations: 0
Alpha: 120 degrees Beta: -240 degrees
Lies in Quadrant II
Reference Angle: 60 degrees
Rotations: 1
Alpha: 240 degrees Beta: -120 degrees
Lies in Quadrant III
Reference Angle: 60 degrees
Rotations: 0
Alpha: 110 degrees Beta: -250 degrees
Lies in Quadrant II
Reference Angle: 70 degrees
Rotations: 0
Alpha: 350 degrees Beta: -10 degrees
Lies in Quadrant IV
Reference Angle: 10 degrees
Rotations: 1
Alpha: 90 degrees Beta: -270 degrees
Quadrantal Angle
Reference Angle: None
9.
Rotations: 2
Alpha: 180 degrees
Beta: -180 degrees
Quadrantal Angle
Reference Angle: None
14. C