1. 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

2. Ray: Starts at a point and extends indefinitely in one direction.B C
Angle: Two rays that are drawn with a
common vertex 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
Terminal
Side
Initial Side
Lies in Quadrant: The location of the terminal side.

3.  = 315 degrees  = 315 degrees  = -45 degrees Lies in Quadrant 4
 (theta) = the angle measurement.
Reference Angle:
The angle between the terminal ray and the x-axis.
1.  = 360 degrees =
1 revolution
2.  = 90 degrees =
¼ revolution
3.  = 180 degrees =
½ revolution
4.  = 260 degrees =
13/18 revolution
Example 1: Draw an angle of 315° in standard position
 = 315 degrees
Initial Side
 = 315 degrees
 = -45 degrees
Terminal Side
Lies in Quadrant 4
Reference: 45 degrees

4.  = -125 degrees  = 235 degrees  = -125 degrees Lies in Quadrant 3
 (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
 = -125 degrees
Initial Side
 = 235 degrees
 = -125 degrees
Terminal Side
Lies in Quadrant 3
Reference: 55 degrees

5.  = 460 degrees  = 100 degrees  = -260 degrees Lies in Quadrant 2
 (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
Terminal Side
 = 460 degrees
 = 100 degrees
Initial Side
 = -260 degrees
Lies in Quadrant 2
Reference: 80 degrees

6.  = -1020 degrees  = 60 degrees  = -300 degrees Lies in Quadrant 1
 (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
Terminal Side
 = degrees
 = 60 degrees
Initial Side
 = -300 degrees
Lies in Quadrant 1
Reference: 60 degrees

7.  = -270 degrees  = 90 degrees  = -270 degrees Quadrantal Angle
 (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 5: Draw an angle of -270° in standard position
Terminal
Side
 = -270 degrees
 = 90 degrees
Initial Side
 = -270 degrees
Quadrantal Angle
Quadrantal Angle: Terminal side is located on an axis

8. Page #3-9 all, 14
Directions (#3-9): Draw the Angle in Standard Position
2. How many complete rotations
3. What are Alpha and Beta
4. What Quadrant does the Angle Lie in
5. What is the Reference Angle

9. Page #3, 4, 6-9 all, 14
Rotations: 0
Alpha: 120 degrees Beta: -240 degrees
Lies in Quadrant II
Reference Angle: 60 degrees
9. Rotations: 2
Alpha: 180 degrees
Beta: -180 degrees
Quadrantal Angle
Reference Angle: None
4. Rotations: 1
Alpha: 240 degrees Beta: -120 degrees
Lies in Quadrant III
Reference Angle: 60 degrees
14. C
6. Rotations: 0
Alpha: 110 degrees Beta: -250 degrees
Lies in Quadrant II
Reference Angle: 70 degrees
7. Rotations: 0
Alpha: 350 degrees Beta: -10 degrees
Lies in Quadrant IV
Reference Angle: 10 degrees
8. Rotations: 1
Alpha: 90 degrees Beta: -270 degrees
Quadrantal Angle
Reference Angle: None